What is 8(x/(2+y))^3-6(x+2y)^2x+12(x+2y)x^2-8x^3 ?

The solution to 8(x/(2+y))^3-6(x+2y)^2x+12(x+2y)x^2-8x^3 is (8x^3)/((2+y)^3)-2x^3-24xy^2

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simplify 8(x/(2+y))^3-6(x+2y)^2x+12(x+2y)x^2-8x^3

simplify

8 (\frac{x}{2 + y})^{3} - 6 (x + 2 y)^{2} x + 12 (x + 2 y) x^{2} - 8 x^{3}

\frac{8 x ^{3}}{( 2 + y ) ^{3}} - 2 x^{3} - 24 x y^{2}

Solution steps

8 (\frac{x}{2 + y})^{3} - 6 (x + 2 y)^{2} x + 12 (x + 2 y) x^{2} - 8 x^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{x}{2 + y})^{3} = \frac{x ^{3}}{( 2 + y ) ^{3}}

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 6 (x + 2 y)^{2} x + 12 (x + 2 y) x^{2} - 8 x^{3}

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 6 x (x + 2 y)^{2} + 12 x^{2} (x + 2 y) - 8 x^{3}

Expand

- 6 x (x + 2 y)^{2} : - 6 x^{3} - 24 x^{2} y - 24 x y^{2}

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 6 x^{3} - 24 x^{2} y - 24 x y^{2} + 12 x^{2} (x + 2 y) - 8 x^{3}

Expand

12 x^{2} (x + 2 y) : 12 x^{3} + 24 x^{2} y

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 6 x^{3} - 24 x^{2} y - 24 x y^{2} + 12 x^{3} + 24 x^{2} y - 8 x^{3}

Add similar elements:

- 24 x^{2} y + 24 x^{2} y = 0

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 6 x^{3} - 24 x y^{2} + 12 x^{3} - 8 x^{3}

Add similar elements:

- 6 x^{3} + 12 x^{3} - 8 x^{3} = - 2 x^{3}

= 8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} - 2 x^{3} - 24 x y^{2}

Simplify

8 \cdot \frac{x ^{3}}{( 2 + y ) ^{3}} : \frac{8 x ^{3}}{( 2 + y ) ^{3}}

= \frac{8 x ^{3}}{( 2 + y ) ^{3}} - 2 x^{3} - 24 x y^{2}

55 x^{4} + 146 x^{2} + 55

\frac{64}{125} \cdot p^{3} - 8 - \frac{96}{25} \cdot p^{2} + \frac{48}{5} \cdot p

a^{10} - a^{8} + a^{6} + a^{4}

35 x y - 55 x^{2} + 10 x

2 x (x + 4) - 3 x (2 x - 5)

What is 8(x/(2+y))^3-6(x+2y)^2x+12(x+2y)x^2-8x^3 ?
The solution to 8(x/(2+y))^3-6(x+2y)^2x+12(x+2y)x^2-8x^3 is (8x^3)/((2+y)^3)-2x^3-24xy^2