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Popular >

expand (t+x-1)^5

Solution

expand

(t + x - 1)^{5}

Solution

t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

Solution steps

(t + x - 1)^{5}

(t + x - 1)^{5} = (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1)

= (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1)

Expand

(t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) (t + x - 1) : t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

= t^{5} + 5 t^{4} x - 5 t^{4} + 10 t^{3} x^{2} - 20 t^{3} x + 10 t^{3} + 10 t^{2} x^{3} - 30 t^{2} x^{2} + 30 t^{2} x - 10 t^{2} + 5 t x^{4} - 20 t x^{3} + 30 t x^{2} - 20 t x + 5 t + x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

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Frequently Asked Questions (FAQ)

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