What is expand (4-x^2-y^2)^2 ?

The solution to expand (4-x^2-y^2)^2 is x^4+y^4-8x^2-8y^2+x^2y^2+y^2x^2+16

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expand (4-x^2-y^2)^2

expand

(4 - x^{2} - y^{2})^{2}

x^{4} + y^{4} - 8 x^{2} - 8 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 16

Solution steps

(4 - x^{2} - y^{2})^{2}

Apply exponent rule:

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

(4 - x^{2} - y^{2})^{2} = (4 - x^{2} - y^{2}) (4 - x^{2} - y^{2})

= (4 - x^{2} - y^{2}) (4 - x^{2} - y^{2})

Distribute parentheses

= 4 \cdot 4 + 4 (- x^{2}) + 4 (- y^{2}) - x^{2} \cdot 4 - x^{2} (- x^{2}) - x^{2} (- y^{2}) - y^{2} \cdot 4 - y^{2} (- x^{2}) - y^{2} (- y^{2})

Simplify

4 \cdot 4 + 4 (- x^{2}) + 4 (- y^{2}) - x^{2} \cdot 4 - x^{2} (- x^{2}) - x^{2} (- y^{2}) - y^{2} \cdot 4 - y^{2} (- x^{2}) - y^{2} (- y^{2}) : x^{4} + y^{4} - 8 x^{2} - 8 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 16

= x^{4} + y^{4} - 8 x^{2} - 8 y^{2} + x^{2} y^{2} + y^{2} x^{2} + 16

x \frac{- 1}{2}

- 4 x^{2} - 4 x^{2}

\frac{4}{3} - \frac{6}{5}

\frac{1}{6} + 7

220 \cdot (- 4) 35

What is expand (4-x^2-y^2)^2 ?
The solution to expand (4-x^2-y^2)^2 is x^4+y^4-8x^2-8y^2+x^2y^2+y^2x^2+16