Question

find the product.$(8w + 4x)(5w - 6x)$a) $40w^{2} - 28wx - 24x^{2}$b) $40w^{2} + 28wx + 24x^{2}$c) $40w^{3} - 28wx - 24wx^{2}$d) $40w^{2} - 28wx + 24x^{2}$

Explanation:

Step1: Apply FOIL method (First terms)

Multiply first terms of each binomial:
$8w \times 5w = 40w^2$

Step2: Apply FOIL method (Outer terms)

Multiply outer terms of the binomials:
$8w \times (-6x) = -48wx$

Step3: Apply FOIL method (Inner terms)

Multiply inner terms of the binomials:
$4x \times 5w = 20wx$

Step4: Apply FOIL method (Last terms)

Multiply last terms of each binomial:
$4x \times (-6x) = -24x^2$

Step5: Combine all terms

Sum the results from Steps 1-4:
$40w^2 - 48wx + 20wx - 24x^2$

Step6: Combine like terms

Simplify the $wx$ terms:
$40w^2 + (-48wx + 20wx) - 24x^2 = 40w^2 - 28wx - 24x^2$

Answer:

A) $40w^2 - 28wx - 24x^2$