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

The solution to expand (x+2y+2z)^2 is x^2+4xy+4xz+4y^2+8yz+4z^2

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

expand

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

x^{2} + 4 x y + 4 x z + 4 y^{2} + 8 yz + 4 z^{2}

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (x + 2 y + 2 z) (x + 2 y + 2 z)

Distribute parentheses

= xx + x \cdot 2 y + x \cdot 2 z + 2 y x + 2 y \cdot 2 y + 2 y \cdot 2 z + 2 z x + 2 z \cdot 2 y + 2 z \cdot 2 z

Simplify

xx + x \cdot 2 y + x \cdot 2 z + 2 y x + 2 y \cdot 2 y + 2 y \cdot 2 z + 2 z x + 2 z \cdot 2 y + 2 z \cdot 2 z : x^{2} + 4 x y + 4 x z + 4 y^{2} + 8 yz + 4 z^{2}

= x^{2} + 4 x y + 4 x z + 4 y^{2} + 8 yz + 4 z^{2}

(- 7) - (- 8)

\frac{1}{45}

\frac{80}{5}

\frac{1}{8} \cdot \frac{6}{7}

What is expand (x+2y+2z)^2 ?
The solution to expand (x+2y+2z)^2 is x^2+4xy+4xz+4y^2+8yz+4z^2