# How do you simplify (y ^ { 3} - 2y ^ { 2} - 3y + 4) - ( 2y ^ { 3} - y ^ { 2} + y - 3)?

Sep 27, 2017

$- {y}^{3} - {y}^{2} - 4 y + 7$

#### Explanation:

So we need to collect all of the like terms, ie. all ${y}^{3}$, ${y}^{2}$ etc. Since there are two brackets we must expand the brackets, since the second bracket:

$\left(- 1\right) \left(2 {y}^{3} - {y}^{2} + y - 3\right)$

So we need to multiply all of the terms inside the brackets by -1, so all of the negative terms become positive and positive terms become negative.

$\left(- 1\right) \left(2 {y}^{3} - {y}^{2} + y - 3\right)$
$- 2 {y}^{3} + {y}^{2} - y + 3$

The first bracket is simply multiplied by 1 so the expanded bracket is:

${y}^{3} - 2 {y}^{2} - 3 y + 4$

${y}^{3} - 2 {y}^{2} - 3 y + 4 - 2 {y}^{3} + {y}^{2} - y + 3$
$- {y}^{3} - {y}^{2} - 4 y + 7$