Đáp án:
Giải thích các bước giải:
`a, x^4 + 1 - 2x^2`
`= (x^2)^2 - 2.x^2.1 +1^2`
`= (x^2 - 1)^2`
`b, x^2 - y^2 + 3y - 3x`
`= (x-y)(x+y)-3(x-y)`
`= (x-y)(x+y-3)`
`c, x^2y +2x^2 - 9y - 18`
`= x^2(y+2) - 9(y+2)`
`= (x^2-9)(y+2)`
`= (x-3)(x+3)(y+2)`
`d, x^4 + 64`
`= (x^2)^2 + 16x^2 + 64 - 16x^2`
`= (x^2)^2 + 2.8.x^2 + 8^2 - 16x^2`
`= (x^2 +8)^2 - (4x)^2`
`= (x^2 + 8 - 4x) (x^2 + 8 + 4x)`
`e, 4x^2 - y^2 + 4x + 1`
`= (4x^2 + 4x + 1) - y^2`
`= [(2x)^2 + 2.2x.1 + 1^2] - y^2`
`= (2x + 1)^2 - y^2`
`= (2x + 1 - y)(2x + 1 + y)`
`f, a^2(b - 1)+b^2(1-b)`
`=a^2(b-1)-b^2(b-1)`
`=(a^2-b^2)(b-1)`
`=(a-b)(a+b)(b-1)`
`g,x^3-y^3-3x^2+3x-1`
`= (x^3 - 3x^2 + 3x - 1) - y^3`
`= (x^3 - 3.x^2.1 + 3.x.1^2 - 1^3) - y^3`
`= (x-1)^3 - y^3`
`= (x-1-y)[(x-1)^2+(x-1)y+y^2]`
`= (x-y-1)(x^2-2x+1+xy-y+y^2]`
`h, 4x^3 - 5x^2 - 16x + 20`
`= x^2(4x-5)-4(4x-5)`
`= (x^2-4)(4x-5)`
`= (x-2)(x+2)(4x-5)`
`i, a^6 + b^6`
`= (a^2)^3 + (b^2)^3`
`= (a^2 + b^2)[(a^2)^2 - a^2b^2 + (b^2)^2]`
`= (a^2 + b^2)(a^4 - a^2b^2 + b^4)`
`k, x^2 + 2x - 8`
`= x^2 + 2x + 1 -9`
`= (x+1)^2 - 3^2`
`=(x+1-3)(x+1+3)`
`=(x-2)(x+4)`
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