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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

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

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

(x - 8) (x - 1)

1 + 3.3 lo g_{10} (25)

\frac{sin ^{2} ( x )}{tan ^{2} ( x )}

g^{2} h 5 g

x^{32} - 1

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