How do you find the product -4d(5d^2-12)+7(d+5)?

May 8, 2017

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 4 d} \left(5 {d}^{2} - 12\right) + \textcolor{b l u e}{7} \left(d + 5\right)$

$\left(\textcolor{red}{- 4 d} \cdot 5 {d}^{2}\right) + \left(\textcolor{red}{- 4 d} \cdot - 12\right) + \left(\textcolor{b l u e}{7} \cdot d\right) + \left(\textcolor{b l u e}{7} \cdot 5\right)$

$- 20 {d}^{3} + 48 d + 7 d + 35$

Now, combine like terms:

$- 20 {d}^{3} + \left(48 + 7\right) d + 35$

$- 20 {d}^{3} + 55 d + 35$