# How do you simplify 2( 4x - 5) + 5( - 2x + 3) as a binomial?

Nov 30, 2017

$5 - 2 x$ or $5 {\left(1 - \frac{2 x}{5}\right)}^{1}$

#### Explanation:

$2 \left(4 x - 5\right) + 5 \left(- 2 x + 3\right) = 8 x - 10 - 10 x + 15$

$= - 2 x + 5 = 5 - 2 x$

If you want to get this in the other binomial form of $a {\left(1 + b x\right)}^{n}$ we must divide both sides by 5:
$5 {\left(1 - \frac{2 x}{5}\right)}^{1}$

This can be proved as ${\left(a + b x\right)}^{n} = {a}^{n} {\left(1 + \frac{b x}{a}\right)}^{n}$

For $n = 1$ we get:
${a}^{n} {\left(1 + \frac{b x}{a}\right)}^{1} = {a}^{1} \left(1 + \frac{b x}{a}\right) = a \left(1 + 1 \left(\frac{b x}{a}\right)\right) = a \left(1 + \frac{b x}{a}\right)$