Question

(lesson 18.2) find each product. (1 point each)

1. $(3 - 2v)(2 - 5v)$
2. $(5x - 4)(3x^{2} + x - 5)$

(lesson 18.2) write a simplified polynomial expression for the situation, then evaluate. (2 points)

1. if the width of a rectangle can be represented by $x$ and the length by $x + 10$, write an expression that can be used to represent the area of the rectangle. simplify the expression as much as possible.

Explanation:

Step1: Apply distributive property (FOIL)

$(3-2v)(2-5v) = 3(2) + 3(-5v) -2v(2) -2v(-5v)$

Step2: Calculate each term

$= 6 -15v -4v +10v^2$

Step3: Combine like terms

$= 10v^2 -19v +6$

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Step1: Apply distributive property

$(5x-4)(3x^2+x-5) = 5x(3x^2+x-5) -4(3x^2+x-5)$

Step2: Expand each product

$= 15x^3 +5x^2 -25x -12x^2 -4x +20$

Step3: Combine like terms

$= 15x^3 -7x^2 -29x +20$

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Step1: Set up area formula

$\text{Area} = \text{width} \times \text{length} = x(x+10)$

Step2: Expand and simplify

$= x^2 +10x$

Answer:

1. $10v^2 -19v +6$
2. $15x^3 -7x^2 -29x +20$
3. $x^2 +10x$