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Popular >

expand (x+3y-2z)^5

Solution

expand

(x + 3 y - 2 z)^{5}

Solution

x^{5} + 15 x^{4} y - 10 x^{4} z + 90 x^{3} y^{2} + 40 x^{3} z^{2} - 120 x^{3} yz + 270 x^{2} y^{3} - 80 x^{2} z^{3} + 360 x^{2} y z^{2} - 540 x^{2} y^{2} z + 405 x y^{4} + 80 x z^{4} - 480 x y z^{3} + 1080 x y^{2} z^{2} - 1080 x y^{3} z + 243 y^{5} - 32 z^{5} + 240 y z^{4} - 720 y^{2} z^{3} + 1080 y^{3} z^{2} - 810 y^{4} z

Solution steps

(x + 3 y - 2 z)^{5}

(x + 3 y - 2 z)^{5} = (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z)

= (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z)

Expand

(x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) (x + 3 y - 2 z) : x^{5} + 15 x^{4} y - 10 x^{4} z + 90 x^{3} y^{2} + 40 x^{3} z^{2} - 120 x^{3} yz + 270 x^{2} y^{3} - 80 x^{2} z^{3} + 360 x^{2} y z^{2} - 540 x^{2} y^{2} z + 405 x y^{4} + 80 x z^{4} - 480 x y z^{3} + 1080 x y^{2} z^{2} - 1080 x y^{3} z + 243 y^{5} - 32 z^{5} + 240 y z^{4} - 720 y^{2} z^{3} + 1080 y^{3} z^{2} - 810 y^{4} z

= x^{5} + 15 x^{4} y - 10 x^{4} z + 90 x^{3} y^{2} + 40 x^{3} z^{2} - 120 x^{3} yz + 270 x^{2} y^{3} - 80 x^{2} z^{3} + 360 x^{2} y z^{2} - 540 x^{2} y^{2} z + 405 x y^{4} + 80 x z^{4} - 480 x y z^{3} + 1080 x y^{2} z^{2} - 1080 x y^{3} z + 243 y^{5} - 32 z^{5} + 240 y z^{4} - 720 y^{2} z^{3} + 1080 y^{3} z^{2} - 810 y^{4} z

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