Question

1. multiply (2x - 1)(x + 6)

a) partial products (in the boxes):
b) expanded (4 terms):
) final answer (simplify/combine like terms):

1. multiply (3x + 4)(x - 2)

partial products (in the boxes):
anded (4 terms): 3x² + 4x - 6x - 8

Explanation:

For (36) Multiply $(2x - 1)(x + 6)$

Step1: Calculate top-left partial product

$x \times 2x = 2x^2$

Step2: Calculate top-right partial product

$x \times (-1) = -x$

Step3: Calculate bottom-left partial product

$6 \times 2x = 12x$

Step4: Calculate bottom-right partial product

$6 \times (-1) = -6$

Step5: List 4 expanded terms

$2x^2 - x + 12x - 6$

Step6: Combine like terms

$2x^2 + (-1+12)x - 6 = 2x^2 + 11x - 6$

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For (37) Multiply $(3x + 4)(x - 2)$

Step1: Correct bottom-right partial product

$-2 \times 4 = -8$

Step2: List correct 4 expanded terms

$3x^2 + 4x - 6x - 8$

Step3: Combine like terms

$3x^2 + (4-6)x - 8 = 3x^2 - 2x - 8$

Answer:

(36)

a) Partial products (top-left, top-right, bottom-left, bottom-right): $2x^2$, $-x$, $12x$, $-6$
b) Expanded (4 terms): $2x^2 - x + 12x - 6$
c) Final simplified answer: $2x^2 + 11x - 6$

(37)

a) Corrected partial products (top-left, top-right, bottom-left, bottom-right): $3x^2$, $4x$, $-6x$, $-8$
b) Corrected expanded (4 terms): $3x^2 + 4x - 6x - 8$
c) Final simplified answer: $3x^2 - 2x - 8$