Đáp án:
`a)(x+1)(y+1)(x-1)(y-1)`
`b)2y(3x^2+y^2)`
`c)3y^2(x+1)^2(x^2-x+1)`
`d)4(x-1+a-y)(x-1-a+y)`
`e)(x+y-1)(x²-xy+y²+x+y+1)`
Giải thích các bước giải:
`a)(xy+1)^2-(x+y)^2`
`=[(xy+1)+(x+y)][(xy+1)-(x+y)]`
`=(xy+1+x+y)(xy+1-x-y)`
`=[(xy+y)+(x+1)][(xy-y)-(x-1)]`
`=[y(x+1)+(x+1)][y(x-1)-(x-1)]`
`=(x+1)(y+1)(x-1)(y-1)`
`b)(x+y)^3-(x-y)^3`
`=[(x+y)-(x-y)][(x+y)^2+(x+y)(x-y)+(x-y)^2]`
`=(x+y-x+y)(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)`
`=2y[(x^2+x^2+x^2)+(2xy-2xy)+(y^2-y^2+y^2)]`
`=2y(3x^2+y^2)`
`c)3x^4y^2+3x^3y^2+3xy^2+3y^2`
`=3y^2(x^4+x^3+x+1)`
`=3y^2[(x^4+x^3)+(x+1)]`
`=3y^2[x^3(x+1)+(x+1)]`
`=3y^2(x+1)(x^3+1)`
`=3y^2(x+1)(x+1)(x^2-x+1)`
`=3y^2(x+1)^2(x^2-x+1)`
`d)4(x^2-y^2)-8(x-ay)-4(a^2-1)`
`=4[x^2-y^2-2(x-ay)-(a^2-1)]`
`=4(x^2-y^2-2x+2ay-a^2+1)`
`=4[(x^2-2x+1)-(a^2-2ay+y^2)]`
`=4[(x-1)^2-(a-y)^2]`
`=4(x-1+a-y)(x-1-a+y)`
`e)(x+y)³-1-3xy(x+y-1)`
`=(x+y-1)[(x+y)²+(x+y).1+1²]-3xy(x+y-1)`
`=(x+y-1)(x²+2xy+y²+x+y+1)-3xy(x+y-1)`
`=(x+y-1)(x²+2xy+y²+x+y+1-3xy)`
`=(x+y-1)(x²-xy+y²+x+y+1)`
