What is the standard form of  y= (-7x-9)^3+(3x-3)^2?

Jan 26, 2018

$y = - 343 {x}^{3} - 1314 {x}^{2} - 1719 x - 720$

Explanation:

Standard form follows the format of $a {x}^{3} + b {x}^{2} + c x + d$. To get in this form, we need to expand everything we can and then combine like-terms

${\left(- 7 x - 9\right)}^{3} + {\left(3 x - 3\right)}^{2}$

$\left(- 7 x - 9\right) \times \left(- 7 x - 9\right) \times \left(- 7 x - 9\right) + \left(3 x - 3\right) \times \left(3 x - 3\right)$

$\left(49 {x}^{2} + 63 x + 63 x + 81\right) \times \left(- 7 x - 9\right) + \left(9 {x}^{2} - 9 x - 9 x + 9\right)$

$\left(49 {x}^{2} + 126 x + 81\right) \times \left(- 7 x - 9\right) + 9 {x}^{2} - 18 x + 9$

$- 343 {x}^{3} - 441 {x}^{2} - 882 {x}^{2} - 1134 x - 567 x - 729 + 9 {x}^{2} - 18 x + 9$

combine like-terms

$- 343 {x}^{3} - 1323 {x}^{2} - 1701 x - 729 + 9 {x}^{2} - 18 x + 9$

$- 343 {x}^{3} - 1314 {x}^{2} - 1719 x - 720$