# How do you simplify (x^2 + 3x + 10)(4x^2 - 2x - 7)?

Jul 17, 2018

$= 4 {x}^{4} + 10 {x}^{3} + 27 {x}^{2} - 41 x - 70$

#### Explanation:

Each term in the first bracket has to be multiplied by each term in the second bracket.

$\left(\textcolor{red}{{x}^{2}} + \textcolor{b l u e}{3 x} + \textcolor{g r e e n}{10}\right) \left(4 {x}^{2} - 2 x - 7\right)$

$= \textcolor{red}{{x}^{2}} \left(4 {x}^{2} - 2 x - 7\right) + \textcolor{b l u e}{3 x} \left(4 {x}^{2} - 2 x - 7\right) + \textcolor{g r e e n}{10} \left(4 {x}^{2} - 2 x - 7\right)$

$= \textcolor{red}{4 {x}^{4} - 2 {x}^{3} - 7 {x}^{2}} + \textcolor{b l u e}{12 {x}^{3} - 6 {x}^{2} - 21 x} + \textcolor{g r e e n}{40 {x}^{2} - 20 x - 70}$

Now simplify by collecting the like terms,

$= \left(4 {x}^{4}\right) + \left(- 2 {x}^{3} + 12 {x}^{3}\right) + \left(- 7 {x}^{2} - 6 {x}^{2} + 40 {x}^{2}\right) + \left(- 21 x - 20 x\right) + \left(- 70\right)$

$= 4 {x}^{4} + 10 {x}^{3} + 27 {x}^{2} - 41 x - 70$