Question

1. what is the area of the rectangle below?

4x - 5
2x + 7

1. a rectangle has an area of $21x^{8}y^{3}$ and a length of $7x^{4}y$. find the expression that represents the width of the rectangle.

Explanation:

Step1: Recall rectangle area formula

Area = length $\times$ width, so $A=(4x-5)(2x+7)$

Step2: Apply FOIL multiplication method

First terms: $4x \times 2x = 8x^2$
Outer terms: $4x \times 7 = 28x$
Inner terms: $-5 \times 2x = -10x$
Last terms: $-5 \times 7 = -35$

Step3: Combine like terms

$8x^2 + 28x -10x -35 = 8x^2 +18x -35$
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Step1: Recall width formula for rectangle

$\text{Width} = \frac{\text{Area}}{\text{Length}}$

Step2: Substitute given expressions

$\text{Width} = \frac{21x^6y^3}{7x^4y}$

Step3: Simplify the expression

Divide coefficients: $\frac{21}{7}=3$
Simplify $x$-terms: $x^{6-4}=x^2$
Simplify $y$-terms: $y^{3-1}=y^2$
Combine: $3x^2y^2$

Answer:

1. For question 20: $8x^2 + 18x - 35$
2. For question 21: $3x^2y^2$