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------------------------------------------------ Relaciona cada multiplicación con su respectivo producto.

1. [tex]4 x^5(8 x^4 + 3 x - 9)[/tex]

2. [tex]2 x^2(10 x^5 - 2 x^3 - x)[/tex]

3. [tex]\frac{20 x^7 - 4 x^5 - 2 x^3}{32 x^9 + 12 x^6 - 36 x^5}[/tex]

4. [tex]-5 x^2(7 x^5 - 4 x^4 + 2 x^3)[/tex]

5. [tex]-3 x^3(x^6 - 11 x^2 - 5)[/tex]

Products:

A. [tex]-3 x^9 + 33 x^5 + 15 x^3[/tex]

B. [tex]-35 x^7 + 20 x^6 - 10 x^5[/tex]

Sure! Let's match each multiplication with its respective product by going through each expression step-by-step.

1. Expression 1:
Multiply: [tex]$4x^5 \left(8x^4 + 3x - 9\right)$[/tex].

Distributing [tex]$4x^5$[/tex] across each term inside the parentheses, we get:
- [tex]$4x^5 \cdot 8x^4 = 32x^9$[/tex]
- [tex]$4x^5 \cdot 3x = 12x^6$[/tex]
- [tex]$4x^5 \cdot (-9) = -36x^5$[/tex]

The product is:
[tex]$32x^9 + 12x^6 - 36x^5$[/tex].

2. Expression 2:
Multiply: [tex]$2x^2 \left(10x^5 - 2x^3 - x\right)$[/tex].

Distributing [tex]$2x^2$[/tex] across each term inside the parentheses, we get:
- [tex]$2x^2 \cdot 10x^5 = 20x^7$[/tex]
- [tex]$2x^2 \cdot (-2x^3) = -4x^5$[/tex]
- [tex]$2x^2 \cdot (-x) = -2x^3$[/tex]

The product is:
[tex]$20x^7 - 4x^5 - 2x^3$[/tex].

3. Expression 3:
Fraction: [tex]$\frac{20x^7 - 4x^5 - 2x^3}{32x^9 + 12x^6 - 36x^5}$[/tex].

This is already simplified in the form of a fraction, so no further simplification is needed.

The product is:
[tex]$\frac{20x^7 - 4x^5 - 2x^3}{32x^9 + 12x^6 - 36x^5}$[/tex].

4. Expression 4:
Multiply: [tex]$-5x^2 \left(7x^5 - 4x^4 + 2x^3\right)$[/tex].

Distributing [tex]$-5x^2$[/tex] across each term inside the parentheses, we get:
- [tex]$-5x^2 \cdot 7x^5 = -35x^7$[/tex]
- [tex]$-5x^2 \cdot (-4x^4) = 20x^6$[/tex]
- [tex]$-5x^2 \cdot 2x^3 = -10x^5$[/tex]

The product is:
[tex]$-35x^7 + 20x^6 - 10x^5$[/tex].

5. Expression 5:
Multiply: [tex]$-3x^3 \left(x^6 - 11x^2 - 5\right)$[/tex].

Distributing [tex]$-3x^3$[/tex] across each term inside the parentheses, we get:
- [tex]$-3x^3 \cdot x^6 = -3x^9$[/tex]
- [tex]$-3x^3 \cdot (-11x^2) = 33x^5$[/tex]
- [tex]$-3x^3 \cdot (-5) = 15x^3$[/tex]

The product is:
[tex]$-3x^9 + 33x^5 + 15x^3$[/tex].

So, each expression is matched with its product as calculated above.