What is expand (a^2+b^2+c^2)^2 ?

The solution to expand (a^2+b^2+c^2)^2 is a^4+a^2b^2+a^2c^2+b^2a^2+b^4+b^2c^2+c^2a^2+c^2b^2+c^4

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expand (a^2+b^2+c^2)^2

expand

(a^{2} + b^{2} + c^{2})^{2}

a^{4} + a^{2} b^{2} + a^{2} c^{2} + b^{2} a^{2} + b^{4} + b^{2} c^{2} + c^{2} a^{2} + c^{2} b^{2} + c^{4}

Solution steps

(a^{2} + b^{2} + c^{2})^{2}

Apply exponent rule:

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

(a^{2} + b^{2} + c^{2})^{2} = (a^{2} + b^{2} + c^{2}) (a^{2} + b^{2} + c^{2})

= (a^{2} + b^{2} + c^{2}) (a^{2} + b^{2} + c^{2})

Distribute parentheses

= a^{2} a^{2} + a^{2} b^{2} + a^{2} c^{2} + b^{2} a^{2} + b^{2} b^{2} + b^{2} c^{2} + c^{2} a^{2} + c^{2} b^{2} + c^{2} c^{2}

Simplify

a^{2} a^{2} + a^{2} b^{2} + a^{2} c^{2} + b^{2} a^{2} + b^{2} b^{2} + b^{2} c^{2} + c^{2} a^{2} + c^{2} b^{2} + c^{2} c^{2} : a^{4} + a^{2} b^{2} + a^{2} c^{2} + b^{2} a^{2} + b^{4} + b^{2} c^{2} + c^{2} a^{2} + c^{2} b^{2} + c^{4}

= a^{4} + a^{2} b^{2} + a^{2} c^{2} + b^{2} a^{2} + b^{4} + b^{2} c^{2} + c^{2} a^{2} + c^{2} b^{2} + c^{4}

- (- 5^{2})

- 1 + (- 8)

2^{l o g_{10} (x)} \cdot 4^{l o g_{10} (x)}

(x + 4) (y - 5)

What is expand (a^2+b^2+c^2)^2 ?
The solution to expand (a^2+b^2+c^2)^2 is a^4+a^2b^2+a^2c^2+b^2a^2+b^4+b^2c^2+c^2a^2+c^2b^2+c^4