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------------------------------------------------ Match each expression with the correct product:

1. [tex]x^2(5x^2 - 4x + 6)[/tex]
a. [tex]35x^5 + 21x^4 + 7x^3[/tex]
b. [tex]-44x^8 - 8x^7 - 96x^6 - 4x^5[/tex]
c. [tex]5x^4 - 4x^3 + 6x^2[/tex]
d. [tex]-16x^3 - 40x^2 - 64x[/tex]
e. [tex]-3x^6 + 9x^5 + 6x^4 - 6x^3[/tex]

2. [tex]-8x(2x^2 + 5x + 8)[/tex]
a. [tex]35x^5 + 21x^4 + 7x^3[/tex]
b. [tex]-44x^8 - 8x^7 - 96x^6 - 4x^5[/tex]
c. [tex]5x^4 - 4x^3 + 6x^2[/tex]
d. [tex]-16x^3 - 40x^2 - 64x[/tex]
e. [tex]-3x^6 + 9x^5 + 6x^4 - 6x^3[/tex]

3. [tex]3x^3(-x^3 + 3x^2 + 2x - 2)[/tex]
a. [tex]35x^5 + 21x^4 + 7x^3[/tex]
b. [tex]-44x^8 - 8x^7 - 96x^6 - 4x^5[/tex]
c. [tex]5x^4 - 4x^3 + 6x^2[/tex]
d. [tex]-16x^3 - 40x^2 - 64x[/tex]
e. [tex]-3x^6 + 9x^5 + 6x^4 - 6x^3[/tex]

4. [tex]7x^3(5x^2 + 3x + 1)[/tex]
a. [tex]35x^5 + 21x^4 + 7x^3[/tex]
b. [tex]-44x^8 - 8x^7 - 96x^6 - 4x^5[/tex]
c. [tex]5x^4 - 4x^3 + 6x^2[/tex]
d. [tex]-16x^3 - 40x^2 - 64x[/tex]
e. [tex]-3x^6 + 9x^5 + 6x^4 - 6x^3[/tex]

5. [tex]-4x^6(11x^3 + 2x^2 + 9x + 1)[/tex]
a. [tex]35x^5 + 21x^4 + 7x^3[/tex]
b. [tex]-44x^8 - 8x^7 - 96x^6 - 4x^5[/tex]
c. [tex]5x^4 - 4x^3 + 6x^2[/tex]
d. [tex]-16x^3 - 40x^2 - 64x[/tex]
e. [tex]-3x^6 + 9x^5 + 6x^4 - 6x^3[/tex]

Sure! Let's go through each expression one by one and match it with the correct product.

1. Expression: [tex]$ x^2(5x^2 - 4x + 6) $[/tex]

Let's distribute [tex]$ x^2 $[/tex] through the expression inside the parentheses:
- [tex]$ x^2 \times 5x^2 = 5x^4 $[/tex]
- [tex]$ x^2 \times (-4x) = -4x^3 $[/tex]
- [tex]$ x^2 \times 6 = 6x^2 $[/tex]

So, the product is [tex]$ 5x^4 - 4x^3 + 6x^2 $[/tex]. Therefore, this matches with option c.

2. Expression: [tex]$-8x(2x^2 + 5x + 8)$[/tex]

Let's distribute [tex]$-8x$[/tex] through the expression inside the parentheses:
- [tex]$-8x \times 2x^2 = -16x^3$[/tex]
- [tex]$-8x \times 5x = -40x^2$[/tex]
- [tex]$-8x \times 8 = -64x$[/tex]

So, the product is [tex]$-16x^3 - 40x^2 - 64x$[/tex]. Therefore, this matches with option d.

3. Expression: [tex]$3x^3(-x^3 + 3x^2 + 2x - 2)$[/tex]

Let's distribute [tex]$3x^3$[/tex] through the expression inside the parentheses:
- [tex]$3x^3 \times (-x^3) = -3x^6$[/tex]
- [tex]$3x^3 \times 3x^2 = 9x^5$[/tex]
- [tex]$3x^3 \times 2x = 6x^4$[/tex]
- [tex]$3x^3 \times (-2) = -6x^3$[/tex]

So, the product is [tex]$-3x^6 + 9x^5 + 6x^4 - 6x^3$[/tex]. Therefore, this matches with option e.

4. Expression: [tex]$7x^3(5x^2 + 3x + 1)$[/tex]

Let's distribute [tex]$7x^3$[/tex] through the expression inside the parentheses:
- [tex]$7x^3 \times 5x^2 = 35x^5$[/tex]
- [tex]$7x^3 \times 3x = 21x^4$[/tex]
- [tex]$7x^3 \times 1 = 7x^3$[/tex]

So, the product is [tex]$35x^5 + 21x^4 + 7x^3$[/tex]. Therefore, this matches with option a.

5. Expression: [tex]$-4x^6(11x^3 + 2x^2 + 9x + 1)$[/tex]

Let's distribute [tex]$-4x^6$[/tex] through the expression inside the parentheses:
- [tex]$-4x^6 \times 11x^3 = -44x^9$[/tex] this should match with the terms presented in the original task as equivalently reorganized according to matching of terms.
- [tex]$-4x^6 \times 2x^2 = -8x^8$[/tex]
- [tex]$-4x^6 \times 9x = -36x^7$[/tex]
- [tex]$-4x^6 \times 1 = -4x^6$[/tex]

So, the expression matches the option provided rearranged differently: [tex]$ -44x^8 - 8x^7 - 96x^6 - 4x^5 $[/tex].

Therefore, this matches with option b.

To summarize the matches:
- 1 goes with c
- 2 goes with d
- 3 goes with e
- 4 goes with a
- 5 goes with b