Đáp án:
`a)4(4x-1)(x-1)`
`b)(3x+2)(9x²-6x+4)`
`c)-x^4y^4(4y+3x)²`
`d)(a+b)(x+y)(a-b)(x-y)`
Giải thích các bước giải:
`a)16x²-8x+1-3(4x-1)`
`=(16x²-8x+1)-3(4x-1)`
`=[(4x)²-2.4x.1+1²]-3(4x-1)`
`=(4x-1)²-3(4x-1)`
`=(4x-1)(4x-1-3)`
`=(4x-1)(4x-4)`
`=4(4x-1)(x-1)`
`b)27x³+8`
`=(3x)³+2³`
`=(3x+2)[(3x)²-3x.2+2²]`
`=(3x+2)(9x²-6x+4)`
`c)-16x^4y^6-24x^5y^5-9x^6y^4`
`=-x^4y^4(16y²+24xy+9x²)`
`=-x^4y^4[(4y)²+2.4y.3x+(3x)²]`
`=-x^4y^4(4y+3x)²`
`d)(ax+by)²-(ay+bx)²`
`=(ax+by+ay+bx)(ax+by-ay-bx)`
`=[(ax+bx)+(ay+by)][(ax-bx)-(ay-by)]`
`=[x(a+b)+y(a+b)][x(a-b)-y(a-b)]`
`=(a+b)(x+y)(a-b)(x-y)`