How do you expand the equation $(4x+y)^4$ using pascals triangle?

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Answer 1 · 2015-09-12T15:19:49

$256x^4 +256x^3y +96x^2y^2 +16xy^3 +y^4$

In the pascals triangle the coefficients 1,4,6,4,1 represent the terms $x^4 +4x^3y +6x^2y^2 +4 xy^3 +y^4$ in the expansion of $(x+y)^4$ .

to write the expansion of (4x+y)^4, replace x by 4x and write

$(4x)^4$ + $4(4x)^3*y$ + $6*(4x)^2*y^2 + 4*(4x)*y^3 +y^4$

On simplification it would be

$256x^4 +256x^3y +96x^2y^2 +16xy^3 +y^4$

How do you expand the equation (4x+y)^4(4x+y)^4 using pascals triangle?