How do I expand the binomial (4x-2y)^4?

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04-06-2018
Mathematics

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How do I expand the binomial (4x-2y)^4?

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caylus caylus · Answer 1 · 2018-06-04T06:10:06+02:00

caylus caylus

04-06-2018

Hi,
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\\\\ (4x-2y)^4=2^4(2x-y)^4\\ =16((2x)^4+4*(2x)^3*(-y)+6(2x)^2*(-y)^2+4(2x)*(-y)^3+(-y)^4)\\ =16*(16x^4-32x^3y+24x^2y^2-8xy^3+y^4)\\\\ =256x^4-512x^3y+384x^2 y^2-128xy^3+16y^4[/tex]

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