# How do you simplify (1 - 2x)(x^2 + 6x + 3)?

Aug 4, 2016

$- 2 {x}^{3} - 11 {x}^{2} + 3$

#### Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.This can be achieved as follows.

$\left(\textcolor{red}{1 - 2 x}\right) \left({x}^{2} + 6 x + 3\right)$

$= \textcolor{red}{1} \left({x}^{2} + 6 x + 3\right) \textcolor{red}{- 2 x} \left({x}^{2} + 6 x + 3\right)$

This shows each term in the 1st bracket multiplying the contents of the 2nd bracket.

now, distribute the brackets.

$\Rightarrow {x}^{2} + 6 x + 3 - 2 {x}^{3} - 12 {x}^{2} - 6 x$

and collecting 'like terms'

$- 2 {x}^{3} + \left({x}^{2} - 12 {x}^{2}\right) + \left(6 x - 6 x\right) + 3$

$= - 2 {x}^{3} - 11 {x}^{2} + 3$

Aug 4, 2016

=$- 2 {x}^{3} - 11 {x}^{2} + 3$

#### Explanation:

Simplify has many possibilities in a question like this:
"Find the product", "Multiply out", "expand" "remove brackets" all mean the same,

Each term (there are 2) in the first bracket has to multiplied by each term (there are 3) in the second bracket. We will end up with 6 terms.

$\left(\textcolor{red}{1} \textcolor{b l u e}{- 2 x}\right) \left({x}^{2} + 6 x + 3\right)$

=$\textcolor{red}{{x}^{2} + 6 x + 3} \textcolor{b l u e}{- 2 {x}^{3} - 12 {x}^{2} - 6 x}$

Now collect like terms.

=color(green)(x^2)+color(magenta)(6x)color(orange)(+3)color(blue)(-2x^3-color(green)(12x^2)+color(magenta)(-6x)

=$- 2 {x}^{3} - 11 {x}^{2} + 3$