Đáp án:
`3)(3-2x)(4x-7)`
`4)(x-2)(6-x)`
`7)(x+3)(x-2)(x-1)(x-3)(x+2)(x+1)`
`8)4(5x+1)(2x-1)`
Giải thích các bước giải:
`3)(x-2)²-(5-3x)²`
`=[(x-2)+(5-3x)][(x-2)-(5-3x)]`
`=(x-2+5-3x)(x-2-5+3x)`
`=(3-2x)(4x-7)`
`4)x²-4-2(x-2)²`
`=(x²-4)-2(x-2)²`
`=(x²-2²)-2(x-2)²`
`=(x+2)(x-2)-2(x-2)²`
`=(x-2)[x+2-2(x-2)]`
`=(x-2)(x+2-2x+4)`
`=(x-2)(6-x)`
`7)x^2(x^2-7)^2-36`
`=[x(x^2-7)]^2-6^2`
`=[x(x^2-7)+6][x(x^2-7)-6]`
`=(x^3-7x+6)(x^3-7x-6)`
`=(x³+3x²-3x²-9x+2x+6)(x³-3x²+3x²-9x+2x-6)`
`=[(x³+3x²)-(3x²+9x)+(2x+6)][(x³-3x²)+(3x²-9x)+(2x-6)]`
`=[x²(x+3)-3x(x+3)+2(x+3)][x²(x-3)+3x(x-3)+2(x-3)]`
`=(x+3)(x²-3x+2)(x-3)(x²+3x+2)`
`=(x+3)(x²-2x-x+2)(x-3)(x²+2x+x+2)`
`=(x+3)[x(x-2)-(x-2)](x-3)[x(x+2)+(x+2)]`
`=(x+3)(x-2)(x-1)(x-3)(x+2)(x+1)`
`8)49x²-(3x+2)²`
`=(7x)²-(3x+2)²`
`=[7x+(3x+2)][7x-(3x+2)]`
`=(7x+3x+2)(7x-3x-2)`
`=(10x+2)(4x-2)`
`=2(5x+1).2(2x-1)`
`=4(5x+1)(2x-1)`
