# Question de480

Jan 7, 2018

$16 {y}^{3}$

#### Explanation:

${x}^{3} + 8 {y}^{3} - 36 x y - 216$ when $x = 2 y + 6$

Substitute in $x = 2 y + 6$

The expression becomes

${\left(2 y + 6\right)}^{3} + 8 {y}^{3} - 36 y \left(2 y + 6\right) - 216$

$= 8 {y}^{3} + 72 {y}^{2} + 216 y + 216 + 8 {y}^{3} - 72 {y}^{2} - 216 y - 216$

Now, we can combine like-terms.

$= 8 {y}^{3} + \cancel{72} {y}^{2} + \cancel{216} y + \cancel{216} + 8 {y}^{3} - \cancel{72} {y}^{2} - \cancel{216} y - \cancel{216}$

$= 16 {y}^{3}$

Jan 7, 2018

0

#### Explanation:

To find the value of an expression, we need to have a single variable.

We can do that by looking at the expression ${x}^{3} + 8 {y}^{3} - 36 x y - 216$, and replacing every x with $2 y + 6$, since $x = 2 y + 6$

${x}^{3} + 8 {y}^{3} - 36 x y - 216$

${\left(2 y + 6\right)}^{3} + 8 {y}^{3} - 36 \left(2 y + 6\right) y - 216$

$\left(8 {y}^{3} + 72 {y}^{2} + 216 y + 216\right) + 8 {y}^{3} + \left(- 72 {y}^{2} - 216 y\right) - 216$

Then simplify by combining like terms.

$16 {y}^{3}$

Isolate y to find value

$16 {y}^{3} = 0$

$\frac{16 {y}^{3}}{16} = \frac{0}{16}$

∛(y^3)=∛0#

$y = 0$

Value is therefore 0