How do you factor # 64x^4 + xy^3#?

1 Answer
Dec 22, 2016

Answer:

#64x^4+xy^3 = x(4x+y)(16x^2-4xy+y^2)#

Explanation:

The sum of cubes identity can be written:

#a^3+b^3 = (a+b)(a^2-ab+b^2)#

Use this with #a=4x# and #b=y# as follows:

#64x^4+xy^3 = x(64x^3+y^3)#

#color(white)(64x^4+xy^3) = x((4x)^3+y^3)#

#color(white)(64x^4+xy^3) = x(4x+y)((4x)^2-(4x)y+y^2)#

#color(white)(64x^4+xy^3) = x(4x+y)(16x^2-4xy+y^2)#