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Popular >

expand (x+y-z)^5

Solution

expand

(x + y - z)^{5}

Solution

x^{5} + 5 x^{4} y - 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} - 20 x^{3} yz + 10 x^{2} y^{3} - 10 x^{2} z^{3} + 30 x^{2} y z^{2} - 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} - 20 x y z^{3} + 30 x y^{2} z^{2} - 20 x y^{3} z + y^{5} - z^{5} + 5 y z^{4} - 10 y^{2} z^{3} + 10 y^{3} z^{2} - 5 y^{4} z

Solution steps

(x + y - z)^{5}

(x + y - z)^{5} = (x + y - z) (x + y - z) (x + y - z) (x + y - z) (x + y - z)

= (x + y - z) (x + y - z) (x + y - z) (x + y - z) (x + y - z)

Expand

(x + y - z) (x + y - z) (x + y - z) (x + y - z) (x + y - z) : x^{5} + 5 x^{4} y - 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} - 20 x^{3} yz + 10 x^{2} y^{3} - 10 x^{2} z^{3} + 30 x^{2} y z^{2} - 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} - 20 x y z^{3} + 30 x y^{2} z^{2} - 20 x y^{3} z + y^{5} - z^{5} + 5 y z^{4} - 10 y^{2} z^{3} + 10 y^{3} z^{2} - 5 y^{4} z

= x^{5} + 5 x^{4} y - 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} - 20 x^{3} yz + 10 x^{2} y^{3} - 10 x^{2} z^{3} + 30 x^{2} y z^{2} - 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} - 20 x y z^{3} + 30 x y^{2} z^{2} - 20 x y^{3} z + y^{5} - z^{5} + 5 y z^{4} - 10 y^{2} z^{3} + 10 y^{3} z^{2} - 5 y^{4} z

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Frequently Asked Questions (FAQ)

What is expand (x+y-z)^5 ?
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