Multiplying Binomials Worksheet Worksheet - Free Printable
Educational worksheet: Multiplying Binomials Worksheet Worksheet. Download and print for classroom or home learning activities.
PNG
1000×1294
121.5 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #979476
⭐
Show Answer Key & Explanations
Step-by-step solution for: Multiplying Binomials Worksheet Worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Multiplying Binomials Worksheet Worksheet
Here are the solutions for the multiplying binomials worksheet. I have worked through each problem step-by-step to ensure accuracy.
1) $(x + 2)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $2 \cdot x = 2x$, $2 \cdot 2 = 4$.
Combine like terms ($2x + 2x = 4x$).
Answer: $x^2 + 4x + 4$
2) $(x - 3)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $-3 \cdot x = -3x$, $-3 \cdot 2 = -6$.
Combine like terms ($2x - 3x = -x$).
Answer: $x^2 - x - 6$
3) $(x - 2)(x - 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -4 = -4x$, $-2 \cdot x = -2x$, $-2 \cdot -4 = 8$.
Combine like terms ($-4x - 2x = -6x$).
Answer: $x^2 - 6x + 8$
4) $(x + 3)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $3 \cdot x = 3x$, $3 \cdot 2 = 6$.
Combine like terms ($2x + 3x = 5x$).
Answer: $x^2 + 5x + 6$
5) $(x - 4)(x - 5)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -5 = -5x$, $-4 \cdot x = -4x$, $-4 \cdot -5 = 20$.
Combine like terms ($-5x - 4x = -9x$).
Answer: $x^2 - 9x + 20$
6) $(x + 5)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $5 \cdot x = 5x$, $5 \cdot 2 = 10$.
Combine like terms ($2x + 5x = 7x$).
Answer: $x^2 + 7x + 10$
7) $(x - 6)(x + 3)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 3 = 3x$, $-6 \cdot x = -6x$, $-6 \cdot 3 = -18$.
Combine like terms ($3x - 6x = -3x$).
Answer: $x^2 - 3x - 18$
8) $(x - 8)(x - 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -4 = -4x$, $-8 \cdot x = -8x$, $-8 \cdot -4 = 32$.
Combine like terms ($-4x - 8x = -12x$).
Answer: $x^2 - 12x + 32$
9) $(x + 2)(x + 8)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 8 = 8x$, $2 \cdot x = 2x$, $2 \cdot 8 = 16$.
Combine like terms ($8x + 2x = 10x$).
Answer: $x^2 + 10x + 16$
10) $(x - 2)(x + 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 4 = 4x$, $-2 \cdot x = -2x$, $-2 \cdot 4 = -8$.
Combine like terms ($4x - 2x = 2x$).
Answer: $x^2 + 2x - 8$
11) $(x + 4)(x + 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 4 = 4x$, $4 \cdot x = 4x$, $4 \cdot 4 = 16$.
Combine like terms ($4x + 4x = 8x$).
Answer: $x^2 + 8x + 16$
12) $(x + 5)(x + 5)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 5 = 5x$, $5 \cdot x = 5x$, $5 \cdot 5 = 25$.
Combine like terms ($5x + 5x = 10x$).
Answer: $x^2 + 10x + 25$
13) $(x - 3)(x + 3)$
This is a difference of squares pattern.
Multiply terms: $x^2 + 3x - 3x - 9$. The middle terms cancel out.
Answer: $x^2 - 9$
14) $(x - 2)(x + 2)$
Difference of squares pattern.
Multiply terms: $x^2 + 2x - 2x - 4$. The middle terms cancel out.
Answer: $x^2 - 4$
15) $(x + 3)(x + 3)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 3 = 3x$, $3 \cdot x = 3x$, $3 \cdot 3 = 9$.
Combine like terms ($3x + 3x = 6x$).
Answer: $x^2 + 6x + 9$
16) $(x + 4)(x + 6)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 6 = 6x$, $4 \cdot x = 4x$, $4 \cdot 6 = 24$.
Combine like terms ($6x + 4x = 10x$).
Answer: $x^2 + 10x + 24$
17) $(x - 7)(x + 7)$
Difference of squares pattern.
Multiply terms: $x^2 + 7x - 7x - 49$. The middle terms cancel out.
Answer: $x^2 - 49$
18) $(x - 7)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $-7 \cdot x = -7x$, $-7 \cdot 2 = -14$.
Combine like terms ($2x - 7x = -5x$).
Answer: $x^2 - 5x - 14$
19) $(2x + 2)(x + 3)$
Multiply terms: $2x \cdot x = 2x^2$, $2x \cdot 3 = 6x$, $2 \cdot x = 2x$, $2 \cdot 3 = 6$.
Combine like terms ($6x + 2x = 8x$).
Answer: $2x^2 + 8x + 6$
20) $(2x - 3)(2x + 4)$
Multiply terms: $2x \cdot 2x = 4x^2$, $2x \cdot 4 = 8x$, $-3 \cdot 2x = -6x$, $-3 \cdot 4 = -12$.
Combine like terms ($8x - 6x = 2x$).
Answer: $4x^2 + 2x - 12$
21) $(x - 8)(2x + 8)$
Multiply terms: $x \cdot 2x = 2x^2$, $x \cdot 8 = 8x$, $-8 \cdot 2x = -16x$, $-8 \cdot 8 = -64$.
Combine like terms ($8x - 16x = -8x$).
Answer: $2x^2 - 8x - 64$
22) $(x - 7)(x - 6)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -6 = -6x$, $-7 \cdot x = -7x$, $-7 \cdot -6 = 42$.
Combine like terms ($-6x - 7x = -13x$).
Answer: $x^2 - 13x + 42$
23) $(x - 8)(x + 8)$
Difference of squares pattern.
Multiply terms: $x^2 + 8x - 8x - 64$. The middle terms cancel out.
Answer: $x^2 - 64$
24) $(3x - 2)(4x + 2)$
Multiply terms: $3x \cdot 4x = 12x^2$, $3x \cdot 2 = 6x$, $-2 \cdot 4x = -8x$, $-2 \cdot 2 = -4$.
Combine like terms ($6x - 8x = -2x$).
Answer: $12x^2 - 2x - 4$
25) $(2x - 5)(x + 7)$
Multiply terms: $2x \cdot x = 2x^2$, $2x \cdot 7 = 14x$, $-5 \cdot x = -5x$, $-5 \cdot 7 = -35$.
Combine like terms ($14x - 5x = 9x$).
Answer: $2x^2 + 9x - 35$
26) $(5x - 4)(3x + 3)$
Multiply terms: $5x \cdot 3x = 15x^2$, $5x \cdot 3 = 15x$, $-4 \cdot 3x = -12x$, $-4 \cdot 3 = -12$.
Combine like terms ($15x - 12x = 3x$).
Answer: $15x^2 + 3x - 12$
27) $(6x + 9)(4x + 9)$
Multiply terms: $6x \cdot 4x = 24x^2$, $6x \cdot 9 = 54x$, $9 \cdot 4x = 36x$, $9 \cdot 9 = 81$.
Combine like terms ($54x + 36x = 90x$).
Answer: $24x^2 + 90x + 81$
28) $(2x - 6)(5x + 6)$
Multiply terms: $2x \cdot 5x = 10x^2$, $2x \cdot 6 = 12x$, $-6 \cdot 5x = -30x$, $-6 \cdot 6 = -36$.
Combine like terms ($12x - 30x = -18x$).
Answer: $10x^2 - 18x - 36$
29) $(x + 4)(4x - 8)$
Multiply terms: $x \cdot 4x = 4x^2$, $x \cdot -8 = -8x$, $4 \cdot 4x = 16x$, $4 \cdot -8 = -32$.
Combine like terms ($-8x + 16x = 8x$).
Answer: $4x^2 + 8x - 32$
30) $(6x - 4)(6x + 4)$
Difference of squares pattern (or standard multiplication).
Multiply terms: $36x^2 + 24x - 24x - 16$. The middle terms cancel out.
Answer: $36x^2 - 16$
31) $(3x + 3)(3x - 4)$
Multiply terms: $3x \cdot 3x = 9x^2$, $3x \cdot -4 = -12x$, $3 \cdot 3x = 9x$, $3 \cdot -4 = -12$.
Combine like terms ($-12x + 9x = -3x$).
Answer: $9x^2 - 3x - 12$
32) $(x^2 + 2)(x^2 - 2)$
Difference of squares pattern. Note that the variable is squared.
Multiply terms: $x^2 \cdot x^2 = x^4$, $x^2 \cdot -2 = -2x^2$, $2 \cdot x^2 = 2x^2$, $2 \cdot -2 = -4$.
The middle terms cancel out.
Answer: $x^4 - 4$
Final Answer:
1) $x^2 + 4x + 4$
2) $x^2 - x - 6$
3) $x^2 - 6x + 8$
4) $x^2 + 5x + 6$
5) $x^2 - 9x + 20$
6) $x^2 + 7x + 10$
7) $x^2 - 3x - 18$
8) $x^2 - 12x + 32$
9) $x^2 + 10x + 16$
10) $x^2 + 2x - 8$
11) $x^2 + 8x + 16$
12) $x^2 + 10x + 25$
13) $x^2 - 9$
14) $x^2 - 4$
15) $x^2 + 6x + 9$
16) $x^2 + 10x + 24$
17) $x^2 - 49$
18) $x^2 - 5x - 14$
19) $2x^2 + 8x + 6$
20) $4x^2 + 2x - 12$
21) $2x^2 - 8x - 64$
22) $x^2 - 13x + 42$
23) $x^2 - 64$
24) $12x^2 - 2x - 4$
25) $2x^2 + 9x - 35$
26) $15x^2 + 3x - 12$
27) $24x^2 + 90x + 81$
28) $10x^2 - 18x - 36$
29) $4x^2 + 8x - 32$
30) $36x^2 - 16$
31) $9x^2 - 3x - 12$
32) $x^4 - 4$
1) $(x + 2)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $2 \cdot x = 2x$, $2 \cdot 2 = 4$.
Combine like terms ($2x + 2x = 4x$).
Answer: $x^2 + 4x + 4$
2) $(x - 3)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $-3 \cdot x = -3x$, $-3 \cdot 2 = -6$.
Combine like terms ($2x - 3x = -x$).
Answer: $x^2 - x - 6$
3) $(x - 2)(x - 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -4 = -4x$, $-2 \cdot x = -2x$, $-2 \cdot -4 = 8$.
Combine like terms ($-4x - 2x = -6x$).
Answer: $x^2 - 6x + 8$
4) $(x + 3)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $3 \cdot x = 3x$, $3 \cdot 2 = 6$.
Combine like terms ($2x + 3x = 5x$).
Answer: $x^2 + 5x + 6$
5) $(x - 4)(x - 5)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -5 = -5x$, $-4 \cdot x = -4x$, $-4 \cdot -5 = 20$.
Combine like terms ($-5x - 4x = -9x$).
Answer: $x^2 - 9x + 20$
6) $(x + 5)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $5 \cdot x = 5x$, $5 \cdot 2 = 10$.
Combine like terms ($2x + 5x = 7x$).
Answer: $x^2 + 7x + 10$
7) $(x - 6)(x + 3)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 3 = 3x$, $-6 \cdot x = -6x$, $-6 \cdot 3 = -18$.
Combine like terms ($3x - 6x = -3x$).
Answer: $x^2 - 3x - 18$
8) $(x - 8)(x - 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -4 = -4x$, $-8 \cdot x = -8x$, $-8 \cdot -4 = 32$.
Combine like terms ($-4x - 8x = -12x$).
Answer: $x^2 - 12x + 32$
9) $(x + 2)(x + 8)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 8 = 8x$, $2 \cdot x = 2x$, $2 \cdot 8 = 16$.
Combine like terms ($8x + 2x = 10x$).
Answer: $x^2 + 10x + 16$
10) $(x - 2)(x + 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 4 = 4x$, $-2 \cdot x = -2x$, $-2 \cdot 4 = -8$.
Combine like terms ($4x - 2x = 2x$).
Answer: $x^2 + 2x - 8$
11) $(x + 4)(x + 4)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 4 = 4x$, $4 \cdot x = 4x$, $4 \cdot 4 = 16$.
Combine like terms ($4x + 4x = 8x$).
Answer: $x^2 + 8x + 16$
12) $(x + 5)(x + 5)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 5 = 5x$, $5 \cdot x = 5x$, $5 \cdot 5 = 25$.
Combine like terms ($5x + 5x = 10x$).
Answer: $x^2 + 10x + 25$
13) $(x - 3)(x + 3)$
This is a difference of squares pattern.
Multiply terms: $x^2 + 3x - 3x - 9$. The middle terms cancel out.
Answer: $x^2 - 9$
14) $(x - 2)(x + 2)$
Difference of squares pattern.
Multiply terms: $x^2 + 2x - 2x - 4$. The middle terms cancel out.
Answer: $x^2 - 4$
15) $(x + 3)(x + 3)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 3 = 3x$, $3 \cdot x = 3x$, $3 \cdot 3 = 9$.
Combine like terms ($3x + 3x = 6x$).
Answer: $x^2 + 6x + 9$
16) $(x + 4)(x + 6)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 6 = 6x$, $4 \cdot x = 4x$, $4 \cdot 6 = 24$.
Combine like terms ($6x + 4x = 10x$).
Answer: $x^2 + 10x + 24$
17) $(x - 7)(x + 7)$
Difference of squares pattern.
Multiply terms: $x^2 + 7x - 7x - 49$. The middle terms cancel out.
Answer: $x^2 - 49$
18) $(x - 7)(x + 2)$
Multiply terms: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $-7 \cdot x = -7x$, $-7 \cdot 2 = -14$.
Combine like terms ($2x - 7x = -5x$).
Answer: $x^2 - 5x - 14$
19) $(2x + 2)(x + 3)$
Multiply terms: $2x \cdot x = 2x^2$, $2x \cdot 3 = 6x$, $2 \cdot x = 2x$, $2 \cdot 3 = 6$.
Combine like terms ($6x + 2x = 8x$).
Answer: $2x^2 + 8x + 6$
20) $(2x - 3)(2x + 4)$
Multiply terms: $2x \cdot 2x = 4x^2$, $2x \cdot 4 = 8x$, $-3 \cdot 2x = -6x$, $-3 \cdot 4 = -12$.
Combine like terms ($8x - 6x = 2x$).
Answer: $4x^2 + 2x - 12$
21) $(x - 8)(2x + 8)$
Multiply terms: $x \cdot 2x = 2x^2$, $x \cdot 8 = 8x$, $-8 \cdot 2x = -16x$, $-8 \cdot 8 = -64$.
Combine like terms ($8x - 16x = -8x$).
Answer: $2x^2 - 8x - 64$
22) $(x - 7)(x - 6)$
Multiply terms: $x \cdot x = x^2$, $x \cdot -6 = -6x$, $-7 \cdot x = -7x$, $-7 \cdot -6 = 42$.
Combine like terms ($-6x - 7x = -13x$).
Answer: $x^2 - 13x + 42$
23) $(x - 8)(x + 8)$
Difference of squares pattern.
Multiply terms: $x^2 + 8x - 8x - 64$. The middle terms cancel out.
Answer: $x^2 - 64$
24) $(3x - 2)(4x + 2)$
Multiply terms: $3x \cdot 4x = 12x^2$, $3x \cdot 2 = 6x$, $-2 \cdot 4x = -8x$, $-2 \cdot 2 = -4$.
Combine like terms ($6x - 8x = -2x$).
Answer: $12x^2 - 2x - 4$
25) $(2x - 5)(x + 7)$
Multiply terms: $2x \cdot x = 2x^2$, $2x \cdot 7 = 14x$, $-5 \cdot x = -5x$, $-5 \cdot 7 = -35$.
Combine like terms ($14x - 5x = 9x$).
Answer: $2x^2 + 9x - 35$
26) $(5x - 4)(3x + 3)$
Multiply terms: $5x \cdot 3x = 15x^2$, $5x \cdot 3 = 15x$, $-4 \cdot 3x = -12x$, $-4 \cdot 3 = -12$.
Combine like terms ($15x - 12x = 3x$).
Answer: $15x^2 + 3x - 12$
27) $(6x + 9)(4x + 9)$
Multiply terms: $6x \cdot 4x = 24x^2$, $6x \cdot 9 = 54x$, $9 \cdot 4x = 36x$, $9 \cdot 9 = 81$.
Combine like terms ($54x + 36x = 90x$).
Answer: $24x^2 + 90x + 81$
28) $(2x - 6)(5x + 6)$
Multiply terms: $2x \cdot 5x = 10x^2$, $2x \cdot 6 = 12x$, $-6 \cdot 5x = -30x$, $-6 \cdot 6 = -36$.
Combine like terms ($12x - 30x = -18x$).
Answer: $10x^2 - 18x - 36$
29) $(x + 4)(4x - 8)$
Multiply terms: $x \cdot 4x = 4x^2$, $x \cdot -8 = -8x$, $4 \cdot 4x = 16x$, $4 \cdot -8 = -32$.
Combine like terms ($-8x + 16x = 8x$).
Answer: $4x^2 + 8x - 32$
30) $(6x - 4)(6x + 4)$
Difference of squares pattern (or standard multiplication).
Multiply terms: $36x^2 + 24x - 24x - 16$. The middle terms cancel out.
Answer: $36x^2 - 16$
31) $(3x + 3)(3x - 4)$
Multiply terms: $3x \cdot 3x = 9x^2$, $3x \cdot -4 = -12x$, $3 \cdot 3x = 9x$, $3 \cdot -4 = -12$.
Combine like terms ($-12x + 9x = -3x$).
Answer: $9x^2 - 3x - 12$
32) $(x^2 + 2)(x^2 - 2)$
Difference of squares pattern. Note that the variable is squared.
Multiply terms: $x^2 \cdot x^2 = x^4$, $x^2 \cdot -2 = -2x^2$, $2 \cdot x^2 = 2x^2$, $2 \cdot -2 = -4$.
The middle terms cancel out.
Answer: $x^4 - 4$
Final Answer:
1) $x^2 + 4x + 4$
2) $x^2 - x - 6$
3) $x^2 - 6x + 8$
4) $x^2 + 5x + 6$
5) $x^2 - 9x + 20$
6) $x^2 + 7x + 10$
7) $x^2 - 3x - 18$
8) $x^2 - 12x + 32$
9) $x^2 + 10x + 16$
10) $x^2 + 2x - 8$
11) $x^2 + 8x + 16$
12) $x^2 + 10x + 25$
13) $x^2 - 9$
14) $x^2 - 4$
15) $x^2 + 6x + 9$
16) $x^2 + 10x + 24$
17) $x^2 - 49$
18) $x^2 - 5x - 14$
19) $2x^2 + 8x + 6$
20) $4x^2 + 2x - 12$
21) $2x^2 - 8x - 64$
22) $x^2 - 13x + 42$
23) $x^2 - 64$
24) $12x^2 - 2x - 4$
25) $2x^2 + 9x - 35$
26) $15x^2 + 3x - 12$
27) $24x^2 + 90x + 81$
28) $10x^2 - 18x - 36$
29) $4x^2 + 8x - 32$
30) $36x^2 - 16$
31) $9x^2 - 3x - 12$
32) $x^4 - 4$
Parent Tip: Review the logic above to help your child master the concept of multiply binomials worksheet.
