Question

1. what is ((5b^{2}+8b + 3)(5b^{2}+6b - 7))?

a. (24b^{4}+70b^{3}+28b^{2}-37b - 21)

b. (25b^{4}+71b^{3}+27b^{2}-38b - 21)

c. (25b^{4}+70b^{3}+27b^{2}-38b - 22)

d. (25b^{4}+70b^{3}+28b^{2}-38b - 21)

Explanation:

Step1: Distribute first polynomial terms

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

Step2: Expand each product term

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

Step3: Combine like terms

Combine $b^3$: $30b^3+40b^3=70b^3$
Combine $b^2$: $-35b^2+48b^2+15b^2=28b^2$
Combine $b$: $-56b+18b=-38b$

Step4: Write final polynomial

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

Answer:

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