Question

maria and jamal each have gardens. the area of marias garden is represented by the expression (8x^2 - 3x). jamals garden is a rectangular plot with the width and length represented by the expressions (3x) and (4x - 2). which expressions give how much bigger or smaller jamals garden is compared to jessicas? choose two correct answers.
expressions: (4x^2 - 9x), (-4x^2 + 3x), (4x^2 - 3x), (12x^2 - 6x - 8x^2 - 3x), (12x^2 - 6x - 8x^2 + 3x)

Explanation:

Step1: Calculate Jamal's garden area

Jamal's garden is a rectangle, so area = width × length.
$\text{Area}_{\text{Jamal}} = 3x(4x - 2) = 12x^2 - 6x$

Step2: Find difference (Jamal - Maria)

Subtract Maria's area from Jamal's area to compare sizes.
$\text{Difference} = (12x^2 - 6x) - (8x^2 - 3x) = 12x^2 -6x -8x^2 +3x$

Step3: Simplify the difference

Combine like terms for the simplified expression.
$\text{Difference} = 4x^2 - 3x$

Step4: Find reverse difference (Maria - Jamal)

Subtract Jamal's area from Maria's area for the other valid expression.
$\text{Reverse Difference} = (8x^2 - 3x) - (12x^2 - 6x) = -4x^2 +3x$

Answer:

$4x^2 - 3x$
$-4x^2 + 3x$