Question

1. which expression is equivalent to ( 72xy - 12x^2 + 16x )?

*hint: test all your answer choices using distribution
a. ( 4x(18y - 3x + 4) )
b. ( 8x(9y - x + 2) )
c. ( 4x(18y - 3x - 4) )
d. ( 8x(9y + x - 2) )

Explanation:

Step1: Distribute option a

$4x(18y - 3x + 4) = 4x \cdot 18y - 4x \cdot 3x + 4x \cdot 4 = 72xy - 12x^2 + 16x$

Step2: Verify match to target

The result equals $72xy - 12x^2 + 16x$

Step3: (Optional) Check other options (confirm mismatch)

$8x(9y - x + 2) = 72xy - 8x^2 + 16x$ (mismatch)
$4x(18y - 3x - 4) = 72xy - 12x^2 - 16x$ (mismatch)
$8x(9y + x - 2) = 72xy + 8x^2 - 16x$ (mismatch)

Answer:

a. $4x(18y - 3x + 4)$