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Popular >

expand (x^2+y^2+z^2)^4

Solution

expand

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

Solution

x^{8} + 4 x^{6} y^{2} + 4 x^{6} z^{2} + 6 x^{4} y^{4} + 6 x^{4} z^{4} + 12 x^{4} y^{2} z^{2} + 4 x^{2} y^{6} + 4 x^{2} z^{6} + 12 x^{2} y^{2} z^{4} + 12 x^{2} y^{4} z^{2} + y^{8} + z^{8} + 4 y^{2} z^{6} + 6 y^{4} z^{4} + 4 y^{6} z^{2}

Solution steps

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

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

Expand

(x^{2} + y^{2} + z^{2}) (x^{2} + y^{2} + z^{2}) (x^{2} + y^{2} + z^{2}) (x^{2} + y^{2} + z^{2}) : x^{8} + 4 x^{6} y^{2} + 4 x^{6} z^{2} + 6 x^{4} y^{4} + 6 x^{4} z^{4} + 12 x^{4} y^{2} z^{2} + 4 x^{2} y^{6} + 4 x^{2} z^{6} + 12 x^{2} y^{2} z^{4} + 12 x^{2} y^{4} z^{2} + y^{8} + z^{8} + 4 y^{2} z^{6} + 6 y^{4} z^{4} + 4 y^{6} z^{2}

= x^{8} + 4 x^{6} y^{2} + 4 x^{6} z^{2} + 6 x^{4} y^{4} + 6 x^{4} z^{4} + 12 x^{4} y^{2} z^{2} + 4 x^{2} y^{6} + 4 x^{2} z^{6} + 12 x^{2} y^{2} z^{4} + 12 x^{2} y^{4} z^{2} + y^{8} + z^{8} + 4 y^{2} z^{6} + 6 y^{4} z^{4} + 4 y^{6} z^{2}

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Frequently Asked Questions (FAQ)

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