# What is the standard form of y= (x+x^2)(6x-3) -(2x+2)^3?

Jan 31, 2016

See explanation...

#### Explanation:

$y = \left(x + {x}^{2}\right) \left(6 x - 3\right) - {\left(2 x + 2\right)}^{3}$

Multiply $x + {x}^{2}$ and $6 x - 3$ using Foil method

So,
$\left(x + {x}^{2}\right) \left(6 x - 3\right) = 6 {x}^{2} - 3 x + 6 {x}^{3} - 3 {x}^{2} = 3 {x}^{2} - 3 x + 6 {x}^{3}$

To,simplify ${\left(2 x + 2\right)}^{3}$ Use the formula(Binomial expansion) ${a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

${\left(2 x + 2\right)}^{3} = 8 {x}^{3} + 24 {x}^{2} + 24 x + 8$

Watch this video to now about the binomial expansion:

So,

$y = \left(3 {x}^{2} - 3 x + 6 {x}^{3}\right) - \left(8 {x}^{3} + 24 {x}^{2} + 24 x + 8\right)$

Change the signs,

$\rightarrow y = 3 {x}^{2} - 3 x + 6 {x}^{3} - 8 {x}^{3} - 24 {x}^{2} - 24 x - 8$

$\rightarrow y = - 21 {x}^{2} - 3 x + 6 {x}^{3} - 8 {x}^{3} - 24 x - 8$

$\rightarrow y = - 21 {x}^{2} - 27 x + 6 {x}^{3} - 8 {x}^{3} - 8$

$\rightarrow y = - 21 {x}^{2} - 27 x - 2 {x}^{3} - 8$

In Standard form:

$\rightarrow y = - 2 {x}^{3} - 21 {x}^{2} - 27 x - 8$