Multiplying Binomials worksheets - Free Printable

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will proceed directly to solving the problems on the worksheet. The worksheet contains 30 problems involving the multiplication of binomials. I will solve each one step-by-step using the FOIL method (First, Outer, Inner, Last) or distribution.

Problem 1: $(-10x - 3)(-5x + 1)$
- First: $(-10x)(-5x) = 50x^2$
- Outer: $(-10x)(1) = -10x$
- Inner: $(-3)(-5x) = 15x$
- Last: $(-3)(1) = -3$
- Combine: $50x^2 - 10x + 15x - 3 = 50x^2 + 5x - 3$

Problem 2: $(-9x - 2)(-4x + 5)$
- First: $(-9x)(-4x) = 36x^2$
- Outer: $(-9x)(5) = -45x$
- Inner: $(-2)(-4x) = 8x$
- Last: $(-2)(5) = -10$
- Combine: $36x^2 - 45x + 8x - 10 = 36x^2 - 37x - 10$

Problem 3: $(-1x - 7)(5x + 4)$
- First: $(-1x)(5x) = -5x^2$
- Outer: $(-1x)(4) = -4x$
- Inner: $(-7)(5x) = -35x$
- Last: $(-7)(4) = -28$
- Combine: $-5x^2 - 4x - 35x - 28 = -5x^2 - 39x - 28$

Problem 4: $(-5x - 8)(2x + 1)$
- First: $(-5x)(2x) = -10x^2$
- Outer: $(-5x)(1) = -5x$
- Inner: $(-8)(2x) = -16x$
- Last: $(-8)(1) = -8$
- Combine: $-10x^2 - 5x - 16x - 8 = -10x^2 - 21x - 8$

Problem 5: $(-7x - 9)(3x + 1)$
- First: $(-7x)(3x) = -21x^2$
- Outer: $(-7x)(1) = -7x$
- Inner: $(-9)(3x) = -27x$
- Last: $(-9)(1) = -9$
- Combine: $-21x^2 - 7x - 27x - 9 = -21x^2 - 34x - 9$

Problem 6: $(-2x - 6)(-5x + 2)$
- First: $(-2x)(-5x) = 10x^2$
- Outer: $(-2x)(2) = -4x$
- Inner: $(-6)(-5x) = 30x$
- Last: $(-6)(2) = -12$
- Combine: $10x^2 - 4x + 30x - 12 = 10x^2 + 26x - 12$

Problem 7: $(-9x - 4)(-1x + 4)$
- First: $(-9x)(-1x) = 9x^2$
- Outer: $(-9x)(4) = -36x$
- Inner: $(-4)(-1x) = 4x$
- Last: $(-4)(4) = -16$
- Combine: $9x^2 - 36x + 4x - 16 = 9x^2 - 32x - 16$

Problem 8: $(-5x - 7)(1x + 2)$
- First: $(-5x)(1x) = -5x^2$
- Outer: $(-5x)(2) = -10x$
- Inner: $(-7)(1x) = -7x$
- Last: $(-7)(2) = -14$
- Combine: $-5x^2 - 10x - 7x - 14 = -5x^2 - 17x - 14$

Problem 9: $(-6x - 9)(2x + 5)$
- First: $(-6x)(2x) = -12x^2$
- Outer: $(-6x)(5) = -30x$
- Inner: $(-9)(2x) = -18x$
- Last: $(-9)(5) = -45$
- Combine: $-12x^2 - 30x - 18x - 45 = -12x^2 - 48x - 45$

Problem 10: $(-8x - 2)(3x + 3)$
- First: $(-8x)(3x) = -24x^2$
- Outer: $(-8x)(3) = -24x$
- Inner: $(-2)(3x) = -6x$
- Last: $(-2)(3) = -6$
- Combine: $-24x^2 - 24x - 6x - 6 = -24x^2 - 30x - 6$

Problem 11: $(-6x - 1)(3x + 1)$
- First: $(-6x)(3x) = -18x^2$
- Outer: $(-6x)(1) = -6x$
- Inner: $(-1)(3x) = -3x$
- Last: $(-1)(1) = -1$
- Combine: $-18x^2 - 6x - 3x - 1 = -18x^2 - 9x - 1$

Problem 12: $(-6x - 10)(3x + 2)$
- First: $(-6x)(3x) = -18x^2$
- Outer: $(-6x)(2) = -12x$
- Inner: $(-10)(3x) = -30x$
- Last: $(-10)(2) = -20$
- Combine: $-18x^2 - 12x - 30x - 20 = -18x^2 - 42x - 20$

Problem 13: $(-3x - 8)(2x + 4)$
- First: $(-3x)(2x) = -6x^2$
- Outer: $(-3x)(4) = -12x$
- Inner: $(-8)(2x) = -16x$
- Last: $(-8)(4) = -32$
- Combine: $-6x^2 - 12x - 16x - 32 = -6x^2 - 28x - 32$

Problem 14: $(-5x - 4)(1x + 1)$
- First: $(-5x)(1x) = -5x^2$
- Outer: $(-5x)(1) = -5x$
- Inner: $(-4)(1x) = -4x$
- Last: $(-4)(1) = -4$
- Combine: $-5x^2 - 5x - 4x - 4 = -5x^2 - 9x - 4$

Problem 15: $(-7x - 2)(3x + 5)$
- First: $(-7x)(3x) = -21x^2$
- Outer: $(-7x)(5) = -35x$
- Inner: $(-2)(3x) = -6x$
- Last: $(-2)(5) = -10$
- Combine: $-21x^2 - 35x - 6x - 10 = -21x^2 - 41x - 10$

Problem 16: $(-4x - 10)(1x + 1)$
- First: $(-4x)(1x) = -4x^2$
- Outer: $(-4x)(1) = -4x$
- Inner: $(-10)(1x) = -10x$
- Last: $(-10)(1) = -10$
- Combine: $-4x^2 - 4x - 10x - 10 = -4x^2 - 14x - 10$

Problem 17: $(-3x - 7)(-4x + 5)$
- First: $(-3x)(-4x) = 12x^2$
- Outer: $(-3x)(5) = -15x$
- Inner: $(-7)(-4x) = 28x$
- Last: $(-7)(5) = -35$
- Combine: $12x^2 - 15x + 28x - 35 = 12x^2 + 13x - 35$

Problem 18: $(-6x - 8)(-1x + 2)$
- First: $(-6x)(-1x) = 6x^2$
- Outer: $(-6x)(2) = -12x$
- Inner: $(-8)(-1x) = 8x$
- Last: $(-8)(2) = -16$
- Combine: $6x^2 - 12x + 8x - 16 = 6x^2 - 4x - 16$

Problem 19: $(-7x - 4)(3x + 4)$
- First: $(-7x)(3x) = -21x^2$
- Outer: $(-7x)(4) = -28x$
- Inner: $(-4)(3x) = -12x$
- Last: $(-4)(4) = -16$
- Combine: $-21x^2 - 28x - 12x - 16 = -21x^2 - 40x - 16$

Problem 20: $(-6x - 3)(4x + 3)$
- First: $(-6x)(4x) = -24x^2$
- Outer: $(-6x)(3) = -18x$
- Inner: $(-3)(4x) = -12x$
- Last: $(-3)(3) = -9$
- Combine: $-24x^2 - 18x - 12x - 9 = -24x^2 - 30x - 9$

Problem 21: $(-4x - 5)(3x + 3)$
- First: $(-4x)(3x) = -12x^2$
- Outer: $(-4x)(3) = -12x$
- Inner: $(-5)(3x) = -15x$
- Last: $(-5)(3) = -15$
- Combine: $-12x^2 - 12x - 15x - 15 = -12x^2 - 27x - 15$

Problem 22: $(-1x - 3)(-5x + 3)$
- First: $(-1x)(-5x) = 5x^2$
- Outer: $(-1x)(3) = -3x$
- Inner: $(-3)(-5x) = 15x$
- Last: $(-3)(3) = -9$
- Combine: $5x^2 - 3x + 15x - 9 = 5x^2 + 12x - 9$

Problem 23: $(-8x - 7)(3x + 4)$
- First: $(-8x)(3x) = -24x^2$
- Outer: $(-8x)(4) = -32x$
- Inner: $(-7)(3x) = -21x$
- Last: $(-7)(4) = -28$
- Combine: $-24x^2 - 32x - 21x - 28 = -24x^2 - 53x - 28$

Problem 24: $(-4x - 8)(3x + 2)$
- First: $(-4x)(3x) = -12x^2$
- Outer: $(-4x)(2) = -8x$
- Inner: $(-8)(3x) = -24x$
- Last: $(-8)(2) = -16$
- Combine: $-12x^2 - 8x - 24x - 16 = -12x^2 - 32x - 16$

Problem 25: $(-2x - 3)(-3x + 2)$
- First: $(-2x)(-3x) = 6x^2$
- Outer: $(-2x)(2) = -4x$
- Inner: $(-3)(-3x) = 9x$
- Last: $(-3)(2) = -6$
- Combine: $6x^2 - 4x + 9x - 6 = 6x^2 + 5x - 6$

Problem 26: $(-10x - 1)(-5x + 1)$
- First: $(-10x)(-5x) = 50x^2$
- Outer: $(-10x)(1) = -10x$
- Inner: $(-1)(-5x) = 5x$
- Last: $(-1)(1) = -1$
- Combine: $50x^2 - 10x + 5x - 1 = 50x^2 - 5x - 1$

Problem 27: $(-2x - 8)(2x + 5)$
- First: $(-2x)(2x) = -4x^2$
- Outer: $(-2x)(5) = -10x$
- Inner: $(-8)(2x) = -16x$
- Last: $(-8)(5) = -40$
- Combine: $-4x^2 - 10x - 16x - 40 = -4x^2 - 26x - 40$

Problem 28: $(-10x - 2)(2x + 5)$
- First: $(-10x)(2x) = -20x^2$
- Outer: $(-10x)(5) = -50x$
- Inner: $(-2)(2x) = -4x$
- Last: $(-2)(5) = -10$
- Combine: $-20x^2 - 50x - 4x - 10 = -20x^2 - 54x - 10$

Problem 29: $(-3x - 9)(3x + 1)$
- First: $(-3x)(3x) = -9x^2$
- Outer: $(-3x)(1) = -3x$
- Inner: $(-9)(3x) = -27x$
- Last: $(-9)(1) = -9$
- Combine: $-9x^2 - 3x - 27x - 9 = -9x^2 - 30x - 9$

Problem 30: $(-8x - 1)(3x + 2)$
- First: $(-8x)(3x) = -24x^2$
- Outer: $(-8x)(2) = -16x$
- Inner: $(-1)(3x) = -3x$
- Last: $(-1)(2) = -2$
- Combine: $-24x^2 - 16x - 3x - 2 = -24x^2 - 19x - 2$

Final Answer:
1) $50x^2 + 5x - 3$
2) $36x^2 - 37x - 10$
3) $-5x^2 - 39x - 28$
4) $-10x^2 - 21x - 8$
5) $-21x^2 - 34x - 9$
6) $10x^2 + 26x - 12$
7) $9x^2 - 32x - 16$
8) $-5x^2 - 17x - 14$
9) $-12x^2 - 48x - 45$
10) $-24x^2 - 30x - 6$
11) $-18x^2 - 9x - 1$
12) $-18x^2 - 42x - 20$
13) $-6x^2 - 28x - 32$
14) $-5x^2 - 9x - 4$
15) $-21x^2 - 41x - 10$
16) $-4x^2 - 14x - 10$
17) $12x^2 + 13x - 35$
18) $6x^2 - 4x - 16$
19) $-21x^2 - 40x - 16$
20) $-24x^2 - 30x - 9$
21) $-12x^2 - 27x - 15$
22) $5x^2 + 12x - 9$
23) $-24x^2 - 53x - 28$
24) $-12x^2 - 32x - 16$
25) $6x^2 + 5x - 6$
26) $50x^2 - 5x - 1$
27) $-4x^2 - 26x - 40$
28) $-20x^2 - 54x - 10$
29) $-9x^2 - 30x - 9$
30) $-24x^2 - 19x - 2$