Đáp án+Giải thích các bước giải:
`a)9x^2 y^2+15x^2 y-21xy^2`
`=3xy(3xy+5x-7y)`
`b)x^4+x^3+x^2+1`
`=(x^4-x^3+x^2)+(x^3-x^2+x)+(x^2-x+1)`
`=x^2(x^2-x+1)+x(x^2-x+1)+(x^2-x+1)`
`=(x^2-x+1)(x^2+x+1)`
`c)x^2 y+xy^2-x-y`
`=(x^2 y+xy^2)-(x+y)`
`=xy(x+y)-(x+y)`
`=(x+y)(xy-1)`
`d)x^3+3x^2+3x+1-27z^3`
`=(x^3+3x^2+3x+1)-27z^3`
`=(x+1)^3-(3z)^3`
`=(x+1-3z)[(x+1)^2+(x+1).3z+(3z)^2]`
`=(x-3z+1)(x^2+2x+1+3xz+3z+9z^2)`
Áp dụng: `a^3+3a^2 b+3ab^2+b^3=(a+b)^3`
`a^3-b^3=(a-b)(a^2+ab+b^2)`
`e)5xy^2-10xyz+5xz^2`
`=5x(y^2-2yz+z^2)`
`=5x(y-z)^2`
Áp dụng: `a^2-2ab+b^2=(a-b)^2`
`f)9(x+5)^2-(x-7)^2`
`=[3(x+5)]^2-(x-7)^2`
`=[3(x+5)-(x-7)][3(x+5)+(x-7)]`
`=(3x+15-x+7)(3x+15+x-7)`
`=(2x+22)(4x+8)`
`=8(x+11)(x+2)`
Áp dụng: `a^2-b^2=(a-b)(a+b)`
