Question

因式分解：8x³+27y³+36x²y+54xy²

kuai

Answer 1

8x^3+27y^3+36x^2y+54xy^2
=(8x^3+27y^3)+(36x^2y+54xy^2)
=(2x+3y)(4x^2+9y^2-6xy)+18xy(2x+3y)
=(2x+3y)[(4x^2+9y^2-6xy)+18xy]
=(2x+3y)(4x^2+9y^2+12xy)
=(2x+3y)(2x+3y)^2
=(2x+3y)^3

Answer 2

立方和公式
(x+y)³=x³+y³+3x²y+3xy²

8x³+27y³+36x²y+54xy²
=（2x）³+（3y）³+3（2x*9y²）+3（4x²*3y）
=（2x+3y）³