What is expand (1+x^2+y^2)^2 ?

The solution to expand (1+x^2+y^2)^2 is x^4+y^4+2x^2+2y^2+x^2y^2+y^2x^2+1

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expand (1+x^2+y^2)^2

expand

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

x^{4} + y^{4} + 2 x^{2} + 2 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 1

Solution steps

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

Apply exponent rule:

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

(1 + x^{2} + y^{2})^{2} = (1 + x^{2} + y^{2}) (1 + x^{2} + y^{2})

= (1 + x^{2} + y^{2}) (1 + x^{2} + y^{2})

Distribute parentheses

= 1 \cdot 1 + 1 \cdot x^{2} + 1 \cdot y^{2} + x^{2} \cdot 1 + x^{2} x^{2} + x^{2} y^{2} + y^{2} \cdot 1 + y^{2} x^{2} + y^{2} y^{2}

Simplify

1 \cdot 1 + 1 \cdot x^{2} + 1 \cdot y^{2} + x^{2} \cdot 1 + x^{2} x^{2} + x^{2} y^{2} + y^{2} \cdot 1 + y^{2} x^{2} + y^{2} y^{2} : x^{4} + y^{4} + 2 x^{2} + 2 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 1

= x^{4} + y^{4} + 2 x^{2} + 2 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 1

(3 + 9 i) (3 - 9 i)

49 \times 5

\frac{7 + 3 i}{5 - 2 i}

i^{404}

\frac{96}{32}

What is expand (1+x^2+y^2)^2 ?
The solution to expand (1+x^2+y^2)^2 is x^4+y^4+2x^2+2y^2+x^2y^2+y^2x^2+1