How do you factor 64x^3 + 27y^364x3+27y3?

1 Answer
Jim G.
Apr 30, 2016

(4x + 3y)(16x^2 -12xy + 9y^2)(4x+3y)(16x2−12xy+9y2)

Explanation:

This expression is a color(blue)" sum of cubes "" and is factorised as follows " sum of cubes and is factorised as follows

color(red)(|bar(ul(color(white)(a/a)color(black)( a^3 + b^3 = (a + b)(a^2 -ab +b^2))color(white)(a/a)|)))

now 64x^3 = (4x)^3" and " 27y^3 = (3y)^3

For factorising purposes a = 4x and b = 3y

rArr 64x^3+27y^3= (4x+3y)(16x^2-12xy+9y^2)

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