Question

分解因式: (1)x^3y^3-x^2y^2-xy+1 (2)x^3+8y^3-2x^2y-4xy^2 (3)4a^2+9b^2-49c^2+12ab

Answer 1

解(1)题 有立方和公式 a³+b³=(a+b)(a²-ab+b²)
原式=x³y³-x²y²-xy+1
=(x³y³+1)-(x²y²+xy)
=(xy+1)(x²y²-xy+1)-xy(xy+1)
=(xy+1)[(x²y²-xy+1)-xy]
=(xy+1)(x²y²-2xy+1)
=(xy+1)(xy-1)²

解(2)题：
原式=x³+8y³-2x²y-4xy²
=(x³+8y³)-(2x²y+4xy²)
=[x³+(2y)³]-2xy(x+2y)
=(x+2y)(x²-2xy+4y²)-2xy(x+2y)
=(x+2y)[(x²-2xy+4y²)-2xy]
=(x+2y)(x²-4xy+4y²)
=(x+2y)(x-2y)²

解(3)题：
原式=4a²+9b²-49c²+12ab
=(4a²+12ab+9b²)-49c²
=(2a+3b)²-(7c)²
=[(2a+3b)+7c][(2a+3b)-7c]
=(2a+3b+7c)(2a+3b-7c)