Algebra worksheet featuring polynomial multiplication problems for practice.

Here are the solutions for the polynomial multiplication problems. I have worked through each one step-by-step to ensure accuracy.

1) $(-4x - 4)(-3x + 4)$
* Multiply First terms: $(-4x) \cdot (-3x) = 12x^2$
* Multiply Outer terms: $(-4x) \cdot (4) = -16x$
* Multiply Inner terms: $(-4) \cdot (-3x) = +12x$
* Multiply Last terms: $(-4) \cdot (4) = -16$
* Combine like terms ($-16x + 12x = -4x$):
$12x^2 - 4x - 16$

2) $(-3x - 2)(8x + 7)$
* First: $(-3x) \cdot (8x) = -24x^2$
* Outer: $(-3x) \cdot (7) = -21x$
* Inner: $(-2) \cdot (8x) = -16x$
* Last: $(-2) \cdot (7) = -14$
* Combine like terms ($-21x - 16x = -37x$):
$-24x^2 - 37x - 14$

3) $(3x + 4)(-4x - 1)$
* First: $(3x) \cdot (-4x) = -12x^2$
* Outer: $(3x) \cdot (-1) = -3x$
* Inner: $(4) \cdot (-4x) = -16x$
* Last: $(4) \cdot (-1) = -4$
* Combine like terms ($-3x - 16x = -19x$):
$-12x^2 - 19x - 4$

4) $(-7x + 4)(3x - 6)$
* First: $(-7x) \cdot (3x) = -21x^2$
* Outer: $(-7x) \cdot (-6) = +42x$
* Inner: $(4) \cdot (3x) = +12x$
* Last: $(4) \cdot (-6) = -24$
* Combine like terms ($42x + 12x = 54x$):
$-21x^2 + 54x - 24$

5) $(-4x - 7)(-2x + 1)$
* First: $(-4x) \cdot (-2x) = 8x^2$
* Outer: $(-4x) \cdot (1) = -4x$
* Inner: $(-7) \cdot (-2x) = +14x$
* Last: $(-7) \cdot (1) = -7$
* Combine like terms ($-4x + 14x = 10x$):
$8x^2 + 10x - 7$

6) $(7x - 7)(8x - 3)$
* First: $(7x) \cdot (8x) = 56x^2$
* Outer: $(7x) \cdot (-3) = -21x$
* Inner: $(-7) \cdot (8x) = -56x$
* Last: $(-7) \cdot (-3) = +21$
* Combine like terms ($-21x - 56x = -77x$):
$56x^2 - 77x + 21$

7) $(7x + 8)(6x + 2)$
* First: $(7x) \cdot (6x) = 42x^2$
* Outer: $(7x) \cdot (2) = 14x$
* Inner: $(8) \cdot (6x) = 48x$
* Last: $(8) \cdot (2) = 16$
* Combine like terms ($14x + 48x = 62x$):
$42x^2 + 62x + 16$

8) $(-3x + 3)(4x + 2)$
* First: $(-3x) \cdot (4x) = -12x^2$
* Outer: $(-3x) \cdot (2) = -6x$
* Inner: $(3) \cdot (4x) = 12x$
* Last: $(3) \cdot (2) = 6$
* Combine like terms ($-6x + 12x = 6x$):
$-12x^2 + 6x + 6$

9) $(-8x - 5)(-8x - 4)$
* First: $(-8x) \cdot (-8x) = 64x^2$
* Outer: $(-8x) \cdot (-4) = +32x$
* Inner: $(-5) \cdot (-8x) = +40x$
* Last: $(-5) \cdot (-4) = +20$
* Combine like terms ($32x + 40x = 72x$):
$64x^2 + 72x + 20$

10) $(-x - 3)(3x + 5)$
* First: $(-x) \cdot (3x) = -3x^2$
* Outer: $(-x) \cdot (5) = -5x$
* Inner: $(-3) \cdot (3x) = -9x$
* Last: $(-3) \cdot (5) = -15$
* Combine like terms ($-5x - 9x = -14x$):
$-3x^2 - 14x - 15$

Final Answer:
1) $12x^2 - 4x - 16$
2) $-24x^2 - 37x - 14$
3) $-12x^2 - 19x - 4$
4) $-21x^2 + 54x - 24$
5) $8x^2 + 10x - 7$
6) $56x^2 - 77x + 21$
7) $42x^2 + 62x + 16$
8) $-12x^2 + 6x + 6$
9) $64x^2 + 72x + 20$
10) $-3x^2 - 14x - 15$