Question

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

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

Explanation:

Step1: Calculate top-left partial product

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

Step2: Calculate top-right partial product

$2x \times 6 = 12x$

Step3: Calculate bottom-left partial product

$-1 \times x = -x$

Step4: Calculate bottom-right partial product

$-1 \times 6 = -6$

Step5: List all 4 expanded terms

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

Step6: Combine like terms

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

Answer:

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