Multiplying Binomials worksheet with 15 algebra problems to solve.

Here are the solutions for each problem. To solve these, we multiply every term in the first parenthesis by every term in the second parenthesis (often called the FOIL method: First, Outer, Inner, Last), and then combine any "like" terms (terms with the same variable and power).

1) $(3n + 2)(n + 3)$
- Multiply: $3n \cdot n = 3n^2$, $3n \cdot 3 = 9n$, $2 \cdot n = 2n$, $2 \cdot 3 = 6$
- Combine: $3n^2 + 9n + 2n + 6$
- Result: $3n^2 + 11n + 6$

2) $(3p - 3)(p - 1)$
- Multiply: $3p \cdot p = 3p^2$, $3p \cdot (-1) = -3p$, $-3 \cdot p = -3p$, $-3 \cdot (-1) = 3$
- Combine: $3p^2 - 3p - 3p + 3$
- Result: $3p^2 - 6p + 3$

3) $(2x + 1)(x - 1)$
- Multiply: $2x \cdot x = 2x^2$, $2x \cdot (-1) = -2x$, $1 \cdot x = x$, $1 \cdot (-1) = -1$
- Combine: $2x^2 - 2x + x - 1$
- Result: $2x^2 - x - 1$

4) $(5x - 2)(5x - 8)$
- Multiply: $5x \cdot 5x = 25x^2$, $5x \cdot (-8) = -40x$, $-2 \cdot 5x = -10x$, $-2 \cdot (-8) = 16$
- Combine: $25x^2 - 40x - 10x + 16$
- Result: $25x^2 - 50x + 16$

5) $(5v + 4)(3v - 6)$
- Multiply: $5v \cdot 3v = 15v^2$, $5v \cdot (-6) = -30v$, $4 \cdot 3v = 12v$, $4 \cdot (-6) = -24$
- Combine: $15v^2 - 30v + 12v - 24$
- Result: $15v^2 - 18v - 24$

6) $(x + 1)(x + 2)$
- Multiply: $x \cdot x = x^2$, $x \cdot 2 = 2x$, $1 \cdot x = x$, $1 \cdot 2 = 2$
- Combine: $x^2 + 2x + x + 2$
- Result: $x^2 + 3x + 2$

7) $(x - 5)(x - 4)$
- Multiply: $x \cdot x = x^2$, $x \cdot (-4) = -4x$, $-5 \cdot x = -5x$, $-5 \cdot (-4) = 20$
- Combine: $x^2 - 4x - 5x + 20$
- Result: $x^2 - 9x + 20$

8) $(x + 5)(3x - 1)$
- Multiply: $x \cdot 3x = 3x^2$, $x \cdot (-1) = -x$, $5 \cdot 3x = 15x$, $5 \cdot (-1) = -5$
- Combine: $3x^2 - x + 15x - 5$
- Result: $3x^2 + 14x - 5$

9) $(3x - y)(x + 2y)$
- Multiply: $3x \cdot x = 3x^2$, $3x \cdot 2y = 6xy$, $-y \cdot x = -xy$, $-y \cdot 2y = -2y^2$
- Combine: $3x^2 + 6xy - xy - 2y^2$
- Result: $3x^2 + 5xy - 2y^2$

10) $(4x - 5)(x - 3)$
- Multiply: $4x \cdot x = 4x^2$, $4x \cdot (-3) = -12x$, $-5 \cdot x = -5x$, $-5 \cdot (-3) = 15$
- Combine: $4x^2 - 12x - 5x + 15$
- Result: $4x^2 - 17x + 15$

11) $(x - 1)(2x + 5)$
- Multiply: $x \cdot 2x = 2x^2$, $x \cdot 5 = 5x$, $-1 \cdot 2x = -2x$, $-1 \cdot 5 = -5$
- Combine: $2x^2 + 5x - 2x - 5$
- Result: $2x^2 + 3x - 5$

12) $(3x - 3)(3x + 2)$
- Multiply: $3x \cdot 3x = 9x^2$, $3x \cdot 2 = 6x$, $-3 \cdot 3x = -9x$, $-3 \cdot 2 = -6$
- Combine: $9x^2 + 6x - 9x - 6$
- Result: $9x^2 - 3x - 6$

13) $(6x + 2y)(6x - 2y)$
- This is a difference of squares pattern $(a+b)(a-b) = a^2 - b^2$.
- Square the first term: $(6x)^2 = 36x^2$
- Square the second term: $(2y)^2 = 4y^2$
- Subtract them: $36x^2 - 4y^2$
- Result: $36x^2 - 4y^2$

14) $(5x - 7)(3x - 4)$
- Multiply: $5x \cdot 3x = 15x^2$, $5x \cdot (-4) = -20x$, $-7 \cdot 3x = -21x$, $-7 \cdot (-4) = 28$
- Combine: $15x^2 - 20x - 21x + 28$
- Result: $15x^2 - 41x + 28$

15) $(-2x + 5)(x - 1)$
- Multiply: $-2x \cdot x = -2x^2$, $-2x \cdot (-1) = 2x$, $5 \cdot x = 5x$, $5 \cdot (-1) = -5$
- Combine: $-2x^2 + 2x + 5x - 5$
- Result: $-2x^2 + 7x - 5$

Final Answer:
1) $3n^2 + 11n + 6$
2) $3p^2 - 6p + 3$
3) $2x^2 - x - 1$
4) $25x^2 - 50x + 16$
5) $15v^2 - 18v - 24$
6) $x^2 + 3x + 2$
7) $x^2 - 9x + 20$
8) $3x^2 + 14x - 5$
9) $3x^2 + 5xy - 2y^2$
10) $4x^2 - 17x + 15$
11) $2x^2 + 3x - 5$
12) $9x^2 - 3x - 6$
13) $36x^2 - 4y^2$
14) $15x^2 - 41x + 28$
15) $-2x^2 + 7x - 5$