What is expand (x^2y^3z+2xy^2)^3 ?

The solution to expand (x^2y^3z+2xy^2)^3 is x^6y^9z^3+6x^5y^8z^2+12x^4y^7z+8x^3y^6

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expand (x^2y^3z+2xy^2)^3

expand

(x^{2} y^{3} z + 2 x y^{2})^{3}

x^{6} y^{9} z^{3} + 6 x^{5} y^{8} z^{2} + 12 x^{4} y^{7} z + 8 x^{3} y^{6}

Solution steps

(x^{2} y^{3} z + 2 x y^{2})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(x^{2} y^{3} z)^{3} + 3 (x^{2} y^{3} z)^{2} \cdot 2 x y^{2} + 3 x^{2} y^{3} z (2 x y^{2})^{2} + (2 x y^{2})^{3} : x^{6} y^{9} z^{3} + 6 x^{5} y^{8} z^{2} + 12 x^{4} y^{7} z + 8 x^{3} y^{6}

= x^{6} y^{9} z^{3} + 6 x^{5} y^{8} z^{2} + 12 x^{4} y^{7} z + 8 x^{3} y^{6}

\frac{x ^{4} - 4 x ^{2}}{x ^{2} - 4 x}

2^{2^{5}}

lo g_{2} (121)

4 x (4 x^{2} - x + 3)

2 (\frac{- 1}{2})

What is expand (x^2y^3z+2xy^2)^3 ?
The solution to expand (x^2y^3z+2xy^2)^3 is x^6y^9z^3+6x^5y^8z^2+12x^4y^7z+8x^3y^6