Algebra worksheet for practicing polynomial multiplication, including problems with binomials and trinomials.

Since I can't view or access images directly, I’ll help you solve the polynomial multiplication problems from your worksheet based on the text you provided. Let’s go through each problem step by step and explain the process.

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A. Multiply

We will use the distributive property (FOIL method for binomials) to multiply each pair of polynomials.

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#### 1. $(7x + 12)(4x + 7)$

Use FOIL:
- First: $7x \cdot 4x = 28x^2$
- Outer: $7x \cdot 7 = 49x$
- Inner: $12 \cdot 4x = 48x$
- Last: $12 \cdot 7 = 84$

Add:
$28x^2 + 49x + 48x + 84 = 28x^2 + 97x + 84$

✔ Answer: $28x^2 + 97x + 84$

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#### 2. $(3x + 10)(3x + 4)$

FOIL:
- $3x \cdot 3x = 9x^2$
- $3x \cdot 4 = 12x$
- $10 \cdot 3x = 30x$
- $10 \cdot 4 = 40$

Add: $9x^2 + 12x + 30x + 40 = 9x^2 + 42x + 40$

✔ Answer: $9x^2 + 42x + 40$

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#### 3. $(10x + 12)(8x + 2)$

FOIL:
- $10x \cdot 8x = 80x^2$
- $10x \cdot 2 = 20x$
- $12 \cdot 8x = 96x$
- $12 \cdot 2 = 24$

Add: $80x^2 + 20x + 96x + 24 = 80x^2 + 116x + 24$

✔ Answer: $80x^2 + 116x + 24$

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#### 4. $(10x + 11)(10x + 4)$

FOIL:
- $10x \cdot 10x = 100x^2$
- $10x \cdot 4 = 40x$
- $11 \cdot 10x = 110x$
- $11 \cdot 4 = 44$

Add: $100x^2 + 40x + 110x + 44 = 100x^2 + 150x + 44$

✔ Answer: $100x^2 + 150x + 44$

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#### 5. $(11x + 11)(2x - 6)$

FOIL:
- $11x \cdot 2x = 22x^2$
- $11x \cdot (-6) = -66x$
- $11 \cdot 2x = 22x$
- $11 \cdot (-6) = -66$

Add: $22x^2 - 66x + 22x - 66 = 22x^2 - 44x - 66$

✔ Answer: $22x^2 - 44x - 66$

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#### 6. $(-12x + 9)(-11x + 6)$

FOIL:
- $-12x \cdot -11x = 132x^2$
- $-12x \cdot 6 = -72x$
- $9 \cdot -11x = -99x$
- $9 \cdot 6 = 54$

Add: $132x^2 - 72x - 99x + 54 = 132x^2 - 171x + 54$

✔ Answer: $132x^2 - 171x + 54$

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#### 7. $(8x + 2)(-5x - 5)$

FOIL:
- $8x \cdot -5x = -40x^2$
- $8x \cdot -5 = -40x$
- $2 \cdot -5x = -10x$
- $2 \cdot -5 = -10$

Add: $-40x^2 - 40x - 10x - 10 = -40x^2 - 50x - 10$

✔ Answer: $-40x^2 - 50x - 10$

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#### 8. $(9x + 9)(-11x - 12)$

FOIL:
- $9x \cdot -11x = -99x^2$
- $9x \cdot -12 = -108x$
- $9 \cdot -11x = -99x$
- $9 \cdot -12 = -108$

Add: $-99x^2 - 108x - 99x - 108 = -99x^2 - 207x - 108$

✔ Answer: $-99x^2 - 207x - 108$

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#### 9. $(-12x + 7)(12x + 7)$

This is a difference of squares: $(a + b)(a - b) = a^2 - b^2$, but here it's $(a + b)(a + b)$ with signs.

Wait: $(-12x + 7)(12x + 7)$ — not quite difference of squares.

Better to FOIL:

- $-12x \cdot 12x = -144x^2$
- $-12x \cdot 7 = -84x$
- $7 \cdot 12x = 84x$
- $7 \cdot 7 = 49$

Add: $-144x^2 - 84x + 84x + 49 = -144x^2 + 0x + 49 = -144x^2 + 49$

✔ Answer: $-144x^2 + 49$

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#### 10. $(3x + 2)(-3x - 10)$

FOIL:
- $3x \cdot -3x = -9x^2$
- $3x \cdot -10 = -30x$
- $2 \cdot -3x = -6x$
- $2 \cdot -10 = -20$

Add: $-9x^2 - 30x - 6x - 20 = -9x^2 - 36x - 20$

✔ Answer: $-9x^2 - 36x - 20$

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#### 11. $(14x - 18)(-16x + 16)$

FOIL:
- $14x \cdot -16x = -224x^2$
- $14x \cdot 16 = 224x$
- $-18 \cdot -16x = 288x$
- $-18 \cdot 16 = -288$

Add: $-224x^2 + 224x + 288x - 288 = -224x^2 + 512x - 288$

✔ Answer: $-224x^2 + 512x - 288$

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#### 12. $(8x - 20)(9x - 11)$

FOIL:
- $8x \cdot 9x = 72x^2$
- $8x \cdot -11 = -88x$
- $-20 \cdot 9x = -180x$
- $-20 \cdot -11 = 220$

Add: $72x^2 - 88x - 180x + 220 = 72x^2 - 268x + 220$

✔ Answer: $72x^2 - 268x + 220$

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#### 13. $(-18x - 20)(-17x - 12)$

FOIL:
- $-18x \cdot -17x = 306x^2$
- $-18x \cdot -12 = 216x$
- $-20 \cdot -17x = 340x$
- $-20 \cdot -12 = 240$

Add: $306x^2 + 216x + 340x + 240 = 306x^2 + 556x + 240$

✔ Answer: $306x^2 + 556x + 240$

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#### 14. $(12x - 18)(15x + 16)$

FOIL:
- $12x \cdot 15x = 180x^2$
- $12x \cdot 16 = 192x$
- $-18 \cdot 15x = -270x$
- $-18 \cdot 16 = -288$

Add: $180x^2 + 192x - 270x - 288 = 180x^2 - 78x - 288$

✔ Answer: $180x^2 - 78x - 288$

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#### 15. $(-16x - 15)(-18x - 8)$

FOIL:
- $-16x \cdot -18x = 288x^2$
- $-16x \cdot -8 = 128x$
- $-15 \cdot -18x = 270x$
- $-15 \cdot -8 = 120$

Add: $288x^2 + 128x + 270x + 120 = 288x^2 + 398x + 120$

✔ Answer: $288x^2 + 398x + 120$

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#### 16. $(-6x + 20)(-17x + 17)$

FOIL:
- $-6x \cdot -17x = 102x^2$
- $-6x \cdot 17 = -102x$
- $20 \cdot -17x = -340x$
- $20 \cdot 17 = 340$

Add: $102x^2 - 102x - 340x + 340 = 102x^2 - 442x + 340$

✔ Answer: $102x^2 - 442x + 340$

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#### 17. $(-11x + 6)(-6x - 20)$

FOIL:
- $-11x \cdot -6x = 66x^2$
- $-11x \cdot -20 = 220x$
- $6 \cdot -6x = -36x$
- $6 \cdot -20 = -120$

Add: $66x^2 + 220x - 36x - 120 = 66x^2 + 184x - 120$

✔ Answer: $66x^2 + 184x - 120$

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#### 18. $(-8x - 11)(-12x - 17)$

FOIL:
- $-8x \cdot -12x = 96x^2$
- $-8x \cdot -17 = 136x$
- $-11 \cdot -12x = 132x$
- $-11 \cdot -17 = 187$

Add: $96x^2 + 136x + 132x + 187 = 96x^2 + 268x + 187$

✔ Answer: $96x^2 + 268x + 187$

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#### 19. $(10x - 9)(-7x + 18)$

FOIL:
- $10x \cdot -7x = -70x^2$
- $10x \cdot 18 = 180x$
- $-9 \cdot -7x = 63x$
- $-9 \cdot 18 = -162$

Add: $-70x^2 + 180x + 63x - 162 = -70x^2 + 243x - 162$

✔ Answer: $-70x^2 + 243x - 162$

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#### 20. $(9x - 13)(15x + 18)$

FOIL:
- $9x \cdot 15x = 135x^2$
- $9x \cdot 18 = 162x$
- $-13 \cdot 15x = -195x$
- $-13 \cdot 18 = -234$

Add: $135x^2 + 162x - 195x - 234 = 135x^2 - 33x - 234$

✔ Answer: $135x^2 - 33x - 234$

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B. Multiply (Polynomials with higher degrees)

Now we move to more complex multiplications involving trinomials and higher-degree terms.

We'll use distributive property: multiply each term in the first polynomial by each term in the second.

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#### 1. $(-5x^2 - 8x + 8)(-9x - 12)$

Distribute each term:

- $-5x^2 \cdot (-9x) = 45x^3$
- $-5x^2 \cdot (-12) = 60x^2$
- $-8x \cdot (-9x) = 72x^2$
- $-8x \cdot (-12) = 96x$
- $8 \cdot (-9x) = -72x$
- $8 \cdot (-12) = -96$

Now combine:
- $x^3$: $45x^3$
- $x^2$: $60x^2 + 72x^2 = 132x^2$
- $x$: $96x - 72x = 24x$
- Constant: $-96$

✔ Answer: $45x^3 + 132x^2 + 24x - 96$

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#### 2. $(5x - 11)(-2x^2 - 11x + 8)$

Distribute:
- $5x \cdot -2x^2 = -10x^3$
- $5x \cdot -11x = -55x^2$
- $5x \cdot 8 = 40x$
- $-11 \cdot -2x^2 = 22x^2$
- $-11 \cdot -11x = 121x$
- $-11 \cdot 8 = -88$

Combine:
- $x^3$: $-10x^3$
- $x^2$: $-55x^2 + 22x^2 = -33x^2$
- $x$: $40x + 121x = 161x$
- Constant: $-88$

✔ Answer: $-10x^3 - 33x^2 + 161x - 88$

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#### 3. $(-6x^2 + 3)(11x^2 + 9x - 8)$

Distribute:
- $-6x^2 \cdot 11x^2 = -66x^4$
- $-6x^2 \cdot 9x = -54x^3$
- $-6x^2 \cdot -8 = 48x^2$
- $3 \cdot 11x^2 = 33x^2$
- $3 \cdot 9x = 27x$
- $3 \cdot -8 = -24$

Combine:
- $x^4$: $-66x^4$
- $x^3$: $-54x^3$
- $x^2$: $48x^2 + 33x^2 = 81x^2$
- $x$: $27x$
- Constant: $-24$

✔ Answer: $-66x^4 - 54x^3 + 81x^2 + 27x - 24$

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#### 4. $(8x^2 + 2x)(8x - 11)$

Distribute:
- $8x^2 \cdot 8x = 64x^3$
- $8x^2 \cdot -11 = -88x^2$
- $2x \cdot 8x = 16x^2$
- $2x \cdot -11 = -22x$

Combine:
- $x^3$: $64x^3$
- $x^2$: $-88x^2 + 16x^2 = -72x^2$
- $x$: $-22x$

✔ Answer: $64x^3 - 72x^2 - 22x$

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#### 5. $(-8x^2 + 10x + 11)(-12x + 8)$

Distribute:
- $-8x^2 \cdot -12x = 96x^3$
- $-8x^2 \cdot 8 = -64x^2$
- $10x \cdot -12x = -120x^2$
- $10x \cdot 8 = 80x$
- $11 \cdot -12x = -132x$
- $11 \cdot 8 = 88$

Combine:
- $x^3$: $96x^3$
- $x^2$: $-64x^2 - 120x^2 = -184x^2$
- $x$: $80x - 132x = -52x$
- Constant: $88$

✔ Answer: $96x^3 - 184x^2 - 52x + 88$

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#### 6. $(-11)(-5x^2 - 3x - 11)$

Distribute $-11$:
- $-11 \cdot -5x^2 = 55x^2$
- $-11 \cdot -3x = 33x$
- $-11 \cdot -11 = 121$

✔ Answer: $55x^2 + 33x + 121$

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#### 7. $(-4x - 5)(-3x^2 - 11x - 2)$

Distribute:
- $-4x \cdot -3x^2 = 12x^3$
- $-4x \cdot -11x = 44x^2$
- $-4x \cdot -2 = 8x$
- $-5 \cdot -3x^2 = 15x^2$
- $-5 \cdot -11x = 55x$
- $-5 \cdot -2 = 10$

Combine:
- $x^3$: $12x^3$
- $x^2$: $44x^2 + 15x^2 = 59x^2$
- $x$: $8x + 55x = 63x$
- Constant: $10$

✔ Answer: $12x^3 + 59x^2 + 63x + 10$

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#### 8. $(-9x^2 + 9x)(4x - 9)$

Distribute:
- $-9x^2 \cdot 4x = -36x^3$
- $-9x^2 \cdot -9 = 81x^2$
- $9x \cdot 4x = 36x^2$
- $9x \cdot -9 = -81x$

Combine:
- $x^3$: $-36x^3$
- $x^2$: $81x^2 + 36x^2 = 117x^2$
- $x$: $-81x$

✔ Answer: $-36x^3 + 117x^2 - 81x$

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#### 9. $(-11x^2 + 6x - 10)(-2x^2 - 10x + 12)$

Multiply each term:

Start with $-11x^2$:
- $-11x^2 \cdot -2x^2 = 22x^4$
- $-11x^2 \cdot -10x = 110x^3$
- $-11x^2 \cdot 12 = -132x^2$

Then $6x$:
- $6x \cdot -2x^2 = -12x^3$
- $6x \cdot -10x = -60x^2$
- $6x \cdot 12 = 72x$

Then $-10$:
- $-10 \cdot -2x^2 = 20x^2$
- $-10 \cdot -10x = 100x$
- $-10 \cdot 12 = -120$

Now combine all:
- $x^4$: $22x^4$
- $x^3$: $110x^3 - 12x^3 = 98x^3$
- $x^2$: $-132x^2 - 60x^2 + 20x^2 = -172x^2$
- $x$: $72x + 100x = 172x$
- Constant: $-120$

✔ Answer: $22x^4 + 98x^3 - 172x^2 + 172x - 120$

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#### 10. $(-5x^2 - 11x)(11x + 5)(-5x + 5)$

This is a triple product. We’ll do two at a time.

First, multiply $(-5x^2 - 11x)(11x + 5)$

Distribute:
- $-5x^2 \cdot 11x = -55x^3$
- $-5x^2 \cdot 5 = -25x^2$
- $-11x \cdot 11x = -121x^2$
- $-11x \cdot 5 = -55x$

Add: $-55x^3 - 25x^2 - 121x^2 - 55x = -55x^3 - 146x^2 - 55x$

Now multiply this result by $(-5x + 5)$:

Let $P = -55x^3 - 146x^2 - 55x$

Now: $P \cdot (-5x + 5)$

Distribute:
- $-55x^3 \cdot -5x = 275x^4$
- $-55x^3 \cdot 5 = -275x^3$
- $-146x^2 \cdot -5x = 730x^3$
- $-146x^2 \cdot 5 = -730x^2$
- $-55x \cdot -5x = 275x^2$
- $-55x \cdot 5 = -275x$

Now combine:
- $x^4$: $275x^4$
- $x^3$: $-275x^3 + 730x^3 = 455x^3$
- $x^2$: $-730x^2 + 275x^2 = -455x^2$
- $x$: $-275x$

✔ Answer: $275x^4 + 455x^3 - 455x^2 - 275x$

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Due to length, I’ll stop here and summarize the pattern.

But if you want me to continue with all B problems, please let me know.

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✔ Summary of Key Steps:

- Use FOIL for binomials.
- Use distributive property for higher-degree polynomials.
- Combine like terms carefully.
- Watch signs!

Would you like me to finish the rest of Part B? Or focus on any specific ones?