Question

multiply the following trinomials.
$(2w^{2}-w+5)(4w^{2}+7w-1)$

Explanation:

Step1: Distribute first trinomial terms

$(2w^2 - w + 5)(4w^2 + 7w - 1) = 2w^2(4w^2 + 7w - 1) - w(4w^2 + 7w - 1) + 5(4w^2 + 7w - 1)$

Step2: Expand each product

$= 8w^4 + 14w^3 - 2w^2 - 4w^3 - 7w^2 + w + 20w^2 + 35w - 5$

Step3: Combine like terms

$= 8w^4 + (14w^3 - 4w^3) + (-2w^2 - 7w^2 + 20w^2) + (w + 35w) - 5$
$= 8w^4 + 10w^3 + 11w^2 + 36w - 5$

Answer:

$8w^4 + 10w^3 + 11w^2 + 36w - 5$