因式分解：8x³+27y³+36x²y+54xy²kuai_数学解答

因式分解：8x³+27y³+36x²y+54xy²
kuai

人气：462 ℃　时间：2020-02-06 06:50:50

解答

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