How do you simplify (15x^2 - 9x + 9) - (13x^2 + 15x + 5) - (-16x^2 + 20x + 16) - (-7x^2 + 10x - 10)?

Jun 9, 2015

The answer is $25 {x}^{2} - 54 x + 22$

Explanation:

Go from left to right. A negative sign in front of a set of parentheses changes the signs of the numbers inside the parentheses.

$\left(15 {x}^{2} - 9 x + 9\right) - \left(13 {x}^{2} + 15 x + 5\right) - \left(- 16 x + 20 x + 16\right) - \left(- 7 {x}^{2} + 10 x - 10\right) =$

$\left(15 {x}^{2} - 9 x + 9\right) + \left(- 13 {x}^{2} - 15 x - 5\right) + \left(16 {x}^{2} - 20 x - 16\right) + \left(7 {x}^{2} - 10 x + 10\right)$

Gather like terms.

$\left(15 {x}^{2} - 13 {x}^{2} + 16 {x}^{2} + 7 {x}^{2}\right) + \left(- 9 x - 15 x - 20 x - 10 x\right) + \left(9 - 5 - 16 + 10\right)$

Simplify.

$25 {x}^{2} - 54 x + 22$