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

The solution to expand (3z+3y^2)^3 is 27z^3+81z^2y^2+81zy^4+27y^6

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

expand

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

27 z^{3} + 81 z^{2} y^{2} + 81 z y^{4} + 27 y^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 z)^{3} + 3 (3 z)^{2} \cdot 3 y^{2} + 3 \cdot 3 z (3 y^{2})^{2} + (3 y^{2})^{3} : 27 z^{3} + 81 z^{2} y^{2} + 81 z y^{4} + 27 y^{6}

= 27 z^{3} + 81 z^{2} y^{2} + 81 z y^{4} + 27 y^{6}

(- 1 - 3 i) (- 1 + 3 i)

2 x - 7 (x + 1)

\frac{5}{7} + \frac{5}{6}

4 \cdot (- 9)

What is expand (3z+3y^2)^3 ?
The solution to expand (3z+3y^2)^3 is 27z^3+81z^2y^2+81zy^4+27y^6