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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

= x^{2} x^{2} + x^{2} y^{2} + x^{2} z^{2} + y^{2} x^{2} + y^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2} + z^{2} y^{2} + z^{2} z^{2}

Simplify

x^{2} x^{2} + x^{2} y^{2} + x^{2} z^{2} + y^{2} x^{2} + y^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2} + z^{2} y^{2} + z^{2} z^{2} : x^{4} + x^{2} y^{2} + x^{2} z^{2} + y^{2} x^{2} + y^{4} + y^{2} z^{2} + z^{2} x^{2} + z^{2} y^{2} + z^{4}

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

\frac{1}{4 - x ^{2}}

\frac{x ^{2} - 7 x + 10}{x - 2} \cdot \frac{x + 10}{x ^{2} - x - 20}

(4 x - 7) (4 x + 7)

\frac{31}{5}

3 \times \frac{1}{4}

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