Đáp án:
Giải thích các bước giải:
1) `(x+1)^2 -(x-1)^2-3(x+1)(x-1)`
`= (x+1+x-1)(x+1-x+1)-3.(x^2-1)`
`= 2x.2-3x^2+3`
`=3x^2-4x-3`
2) `5(x+2).(x-2)-\frac{1}{2}.(6-8x)^2+17`
`=5(x^2-4)-\frac{1}{2}.(36-96x+64x^2)+17`
`=5x^2-20-18+48x-32x^2+17`
`=27x^2-48x+21`
3) `(x+y)^2-(x-y)^2`
`=x^2+2xy+y^2-x^2+2xy-y^2`
`=4xy`
4) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2=2x^2-2y^2+x^2+2xy+y^2+x^2-2xy+y^2=3\left(x^2-y^2\right)\)
5) (x - y + z)2 + (z - y)2 + 2(x - y + z)(y - z)
= (x - y + z)2 + 2(x - y + z)(y - z) + (y - z)2
= (x - y + z + y - z)2
= x2
6) `3x(x+2)^2+(x+3)(x-1)(x+1)-(2x-3)^2`
`=3x(x^2+4x+4)+(x+3)(x^2-1)-(4x^2-12x+9)`
`=3x^3+12x^2+12x+x^3-x+3x^2-3-4x^2+12x-9`
`=4x^3+11x^2+23x-12`
7) `(x-3)(x+3)(x+7)-(x-1)(x^2-3)-5x(x+4)^2-(x-5)^2`
`=(x^2-9)(x+7)-(x^3-3x-x^2+3)-5x(x^2+8x+16)-(x^2-10x+25)`
`=x^3+7x^2-9x-63-x^3+3x+x^2-3-5x^3-40x^2-80x-x^2+10x-25`
`=-5x^3-33x^2-76x-91`
8) `2x(x-4)^2-(x+5)(x-7)(x+7)+2(x+5)^2-(x-1)^2`
`=2x(x^2-8x+16)-(x-5)(x^2-49)+2(x^2+10x+25)-(x^2-2x+1)`
`=2x^3-16x^2+32x-x^3+49x+5x^2-245+2x^2+20x+50-x^2+2x-1`
`=x^3-10x^2+103x-196`
