How do you expand ${(2 x - y)}^{5}$ $(2x-y)^5$ using Pascal’s Triangle?

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How do you expand ${(2 x - y)}^{5}$ $(2x-y)^5$ using Pascal’s Triangle?

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Answer 1 · 2016-01-12T15:39:15

$32 x^{5} - 80 x^{4} y + 80 x^{3} y^{2} - 40 x^{2} y^{3} + 10 x y^{4} - y^{5}$ $32x^5 -80x^4y +80x^3y^2 -40x^2y^3 +10xy^4 -y^5$

Explanation:

For n=5, the binomial expansion of ${(a + b)}^{5}$ $(a+b)^5$ given in the 6th row of Pascal triangle is $a^{5} + 5 a^{4} b + 10 a^{3} b^{2} + 10 a^{2} b^{3} + 5 a b^{4} + b^{5}$ $a^5 +5a^4b +10a^3b^2+10a^2b^3+5ab^4 +b^5$ . Now to expand the given binomial, plug in a=2x, b=-y to get the desired value. It would be $32 x^{5} - 80 x^{4} y + 80 x^{3} y^{2} - 40 x^{2} y^{3} + 10 x y^{4} - y^{5}$ $32x^5 -80x^4y +80x^3y^2 -40x^2y^3 +10xy^4 -y^5$

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How do you expand ${(2 x - y)}^{5}$ $(2x-y)^5$ using Pascal’s Triangle?

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How do you expand ${(2 x - y)}^{5}$ $(2x-y)^5$ using Pascal’s Triangle?