Đáp án + Giải thích các bước giải:
`1, (2x+1)^2-(x-3)(x+3)`
`=[(2x)^2+2.2x.1+1^2]-(x^2-3^2)`
`=4x^2+4x+1-x^2+9`
`=3x^2+4x+10`
`2.(x-3y)(x+3y)+(x-y)^2`
`=[x^2-(3y)^2]+(x^2-2.x.y+y^2)`
`=x^2-9y^2+x^2-2xy+y^2`
`=(x^2+x^2)-(9y^2-y^2)-2xy`
`=2x^2-8y^2-2xy`
`3.(2x+5)^2-1`
`=(2x+5)^2-1^2`
`=(2x+5-1)(2x+5+1)`
`=(2x+4)(2x+6)`
`4. (x+3)^2-(x-7)^2`
`=[(x+3)-(x-7)][(x+3)+(x-7)]`
`=(x+3-x+7)(x+3+x-7)`
`=10(2x-4)`
`=20x-40`
`5. (2x+3)^2-(x-1)^2`
`=[(2x+3)-(x-1)][(2x+3)+(x-1)]`
`=(2x+3-x+1)(2x+3+x-1)`
`=(x+4)(3x+2)`
`=3x^2+2x+12x+8`
`=3x^2+14x+8`
`6. (x-2)(x+2)-x(x+3)`
`=x^2-4-x^2-3x`
`=(x^2-x^2)-4-3x`
`=-4-3x`
`7. (2x+1)^2-(3-2x)^2+4`
`=[(2x+1)-(3-2x)][(2x+1)+(3-2x)]+4`
`=(2x+1-3+2x)(2x+1+3-2x)+4`
`=4(4x-2)+4`
`=16x-8+4`
