Question

what is ((5b^2 + 8b + 3)(5b^2 + 6b - 7))?
a. (25b^4 + 71b^3 + 27b^2 - 38b - 21)
b. (24b^4 + 70b^3 + 28b^2 - 37b - 21)
c. (25b^4 + 70b^3 + 27b^2 - 38b - 22)
d. (25b^4 + 70b^3 + 28b^2 - 38b - 21)

Explanation:

Step1: Expand using distributive property

$(5b^2+8b+3)(5b^2+6b-7) = 5b^2(5b^2+6b-7) + 8b(5b^2+6b-7) + 3(5b^2+6b-7)$

Step2: Calculate each term

$5b^2(5b^2+6b-7) = 25b^4 + 30b^3 - 35b^2$
$8b(5b^2+6b-7) = 40b^3 + 48b^2 - 56b$
$3(5b^2+6b-7) = 15b^2 + 18b - 21$

Step3: Combine like terms

$25b^4 + (30b^3+40b^3) + (-35b^2+48b^2+15b^2) + (-56b+18b) -21$

Step4: Simplify the expression

$25b^4 + 70b^3 + 28b^2 - 38b - 21$

Answer:

d. $25b^4 + 70b^3 + 28b^2 - 38b - 21$