What is expand 2(x+piy)^5 ?

The solution to expand 2(x+piy)^5 is 2x^5+10pix^4y+20pi^2x^3y^2+20pi^3x^2y^3+10pi^4xy^4+2pi^5y^5

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expand 2(x+piy)^5

expand

2 (x + π y)^{5}

2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

Solution steps

2 (x + π y)^{5}

(x + π y)^{5} = x^{5} + 5 π x^{4} y + 10 π^{2} x^{3} y^{2} + 10 π^{3} x^{2} y^{3} + 5 π^{4} x y^{4} + π^{5} y^{5}

= 2 (x^{5} + 5 π x^{4} y + 10 π^{2} x^{3} y^{2} + 10 π^{3} x^{2} y^{3} + 5 π^{4} x y^{4} + π^{5} y^{5})

Distribute parentheses

= 2 x^{5} + 2 \cdot 5 π x^{4} y + 2 \cdot 10 π^{2} x^{3} y^{2} + 2 \cdot 10 π^{3} x^{2} y^{3} + 2 \cdot 5 π^{4} x y^{4} + 2 π^{5} y^{5}

Simplify

2 x^{5} + 2 \cdot 5 π x^{4} y + 2 \cdot 10 π^{2} x^{3} y^{2} + 2 \cdot 10 π^{3} x^{2} y^{3} + 2 \cdot 5 π^{4} x y^{4} + 2 π^{5} y^{5} : 2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

= 2 x^{5} + 10 π x^{4} y + 20 π^{2} x^{3} y^{2} + 20 π^{3} x^{2} y^{3} + 10 π^{4} x y^{4} + 2 π^{5} y^{5}

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What is expand 2(x+piy)^5 ?
The solution to expand 2(x+piy)^5 is 2x^5+10pix^4y+20pi^2x^3y^2+20pi^3x^2y^3+10pi^4xy^4+2pi^5y^5