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

The solution to expand (x^2+2xy+y^2)^2 is x^4+y^4+5x^2y^2+y^2x^2+4x^3y+4xy^3

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

expand

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

x^{4} + y^{4} + 5 x^{2} y^{2} + y^{2} x^{2} + 4 x^{3} y + 4 x y^{3}

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

= x^{2} x^{2} + x^{2} \cdot 2 x y + x^{2} y^{2} + 2 x y x^{2} + 2 x y \cdot 2 x y + 2 x y y^{2} + y^{2} x^{2} + y^{2} \cdot 2 x y + y^{2} y^{2}

Simplify

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

= x^{4} + y^{4} + 5 x^{2} y^{2} + y^{2} x^{2} + 4 x^{3} y + 4 x y^{3}

80 (\frac{π}{180})

15 x - 30

\frac{\frac{5}{13}}{- \frac{12}{13}}

41296

4 \cdot \frac{41}{2} - 5 y

What is expand (x^2+2xy+y^2)^2 ?
The solution to expand (x^2+2xy+y^2)^2 is x^4+y^4+5x^2y^2+y^2x^2+4x^3y+4xy^3