# How do you Subtract (-16x^2 - 19x - 10) from (-18x^2 - 13x - 14)?

May 2, 2018

"Subtract A from B" is the same as "Find B - A". First, you need to distribute the negative though the terms of the A part, then combine the results for like terms (terms of the same power of x).

#### Explanation:

$\left(- 18 {x}^{2} - 13 x - 14\right) - \left(- 16 {x}^{2} - 19 x - 10\right) =$
$\left(- 18 {x}^{2} - 13 x - 14\right) + \left(16 {x}^{2} + 19 x + 10\right) =$
$\left(- 18 {x}^{2} + 16 {x}^{2}\right) + \left(- 13 x + 19 x\right) + \left(- 14 + 10\right) =$
$- 2 {x}^{2} + 6 x - 4$

May 2, 2018

$- 2 {x}^{2} + 6 x - 4$

#### Explanation:

Subtracting ( $- 16 {x}^{2} - 19 x - 10$ ) from ( $- 18 {x}^{2} - 13 x - 14$ ) is same as subtracting 5 from 49. (I just mean any two real numbers).

We do something like this:
=49-5
=44

Similarly, we do the subtraction of polynomials but only between numbers with same coefficients.

We'll start like this:

= $\left(- 18 {x}^{2} - 13 x - 14\right) - \left(- 16 {x}^{2} - 19 x - 10\right)$
= $- 18 {x}^{2} - 13 x - 14 + 16 {x}^{2} + 19 x + 10$
= $\left(- 18 + 16\right) {x}^{2} + \left(- 13 + 19\right) x + \left(- 14 + 10\right)$
= $- 2 {x}^{2} + 6 x - 4$

HAPPY LEARNING !!