Question

HELP DUE TODAY! Determine if the problem is done correctly AND explain your reasoning. If the problem is correct then explain the steps that were taken. If the problem is incorrect then explain what the mistake made was and what the correct solution should be.
Multiply the polynomials using the distribution method: (2x – 3)(4x + 8)

Answer 1

Line 2 is correct because of the distribution rule. You multiply each outer term by the inner terms in the parenthesis.

2x(4x+8) = 2x*4x + 2x*8 = 8x^2+16x

-3*(4x+8) = -3*4x-3*8 = -12x-24

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Line 3 is correct as well. The 16x and -12x combine to 4x. You can think of it like 16-12 = 4, then just tack x's onto everything getting 16x-12x = 4x

Or you can think of it like "16 boxes - 12 boxes = 4 boxes" and you replace "boxes" with "x" for shorthand.

The other terms aren't like terms so we just leave them as is.