Đáp án+Giải thích các bước giải:
Bài 3:
`a)(2x+1)^2+(2x+3)^2-2.(2x+1)(2x+3)`
`=(2x+1+2x+3)^2`
`=(4x+4)^2`
`=16x^2+32x+16`
`b) (2x-3)(2x+3)-(x+5)^2-(x-1)(x+2)`
`=4x^2-9-x^2-10x-25-x^2-2x+x+2`
`=2x^2-11x-32`
`c) (24x^2y^3z^2-12x^3y^2z^3+36x^2y^2z^2):(-6x^2y^2z^2)`
`=[24x^2y^3z^2:(-6x^2y^2z^2)]-[12x^3y^2z^3:(-6x^2y^2z^2)]+[36x^2y^2z^2:(-6x^2y^2z^2)]`
`= -4y + 2xz - 6`
`d) (x+2y)(x^2-2xy+4y^2)-(x-y)(x^2+xy+y^2)`
`=(x^3+8y^3)-(x^3-y^3)`
`= x^3+8y^3-x^3+y^3`
`= 9y^3`
`e) (x^3+4x^2-x-4):(x+4)`
`=[x^2(x+4)-(x+4)]:(x+4)`
`=[(x+4)(x^2-1)]:(x+4)`
`= x^2 -1`
`f) x^2(x+y)+y^2(x+y)+2x^2y+2xy^2`
`=x^2(x+y)+y^2(x+y)+2xy(x+y)`
`=(x+y)(x^2+y^2+2xy)`
`=(x+y)(x+y)^2`
`=(x+y)^3`
`g) (x+y)^2-(x-y)^2-2(x-y)(x+y)`
`=[(x+y)-(x-y)]^2`
`=(x+y-x+y)^2`
`= (2y)^2`
`= 4y^2`
`h) (a+b)^3-(a-b)^3-2b^3`
`= (a^3 + 3a^2b + 3ab^2 + b^3) – (a^3 – 3a^2b + 3ab^2 – b^3) – 2b^3`
`= a^3 + 3a^2b + 3ab^2 + b^3 – a^3 + 3a^2b – 3ab^2 + b^3 – 2b^3`
`= (a^3 – a^3) + (3a^2b + 3a^2b) + (3ab^2 – 3ab^2) + (b^3 + b^3 – 2b^3)`
`= 6a^2b`
`i) (x-y)(x+y)(x^2+y^2)(x^4+y^4)`
`=(x^2-y^2)(x^2+y^2)(x^4+y^4)`
`=(x^4-y^4)(x^4+y^4)`
`=x^8-y^8`
