Question

1 multiple choice 34 points which expression is equivalent to \\((h^2 + 9h - 1)(-4h + 3)\\)? \\(\bigcirc -4h^3 - 39h^2 + 23h + 3\\) \\(\bigcirc 4h^3 + 33h^2 - 31h + 3\\) \\(\bigcirc -4h^3 - 33h^2 + 31h - 3\\) \\(\bigcirc 4h^3 + 39h^2 - 23h - 3\\) 2 fill in the blank 15 points determine each product. 19. \\((2x - 7)(5x^2 - 1)\\) type your answer... type your answer... answer type y

Explanation:

Step1: Distribute $h^2$ to $(-4h+3)$

$h^2(-4h + 3) = -4h^3 + 3h^2$

Step2: Distribute $9h$ to $(-4h+3)$

$9h(-4h + 3) = -36h^2 + 27h$

Step3: Distribute $-1$ to $(-4h+3)$

$-1(-4h + 3) = 4h - 3$

Step4: Combine all terms

$-4h^3 + 3h^2 - 36h^2 + 27h + 4h - 3$

Step5: Combine like terms

$-4h^3 + (3h^2-36h^2) + (27h+4h) - 3 = -4h^3 -33h^2 +31h -3$

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Step1: Distribute $2x$ to $(5x^2-1)$

$2x(5x^2 - 1) = 10x^3 - 2x$

Step2: Distribute $-7$ to $(5x^2-1)$

$-7(5x^2 - 1) = -35x^2 + 7$

Step3: Combine all terms

$10x^3 - 2x -35x^2 +7$

Step4: Rearrange in standard form

$10x^3 -35x^2 -2x +7$

Answer:

1. $-4h^3 - 33h^2 + 31h - 3$
2. $10x^3 - 35x^2 - 2x + 7$