50 điểm luôn nhé 2) Rút gọn các biểu thức sau: a) (x + y)2 - (x - y)2 b) (a + b)3 + (a - b)3 - 2a3 3) Phân tích các đa thức sau thành nhân tử: a) x2 - y2 - 2x + 2y b) 2x + 2y - x2 - xy c) 3a2 - 6ab + 3b2 - 12c2 d) x2 - 25 + y2 + 2xy e) a2 + 2ab + b2 - ac - bc f) x2 - 2x - 4y2 - 4y g) x2y - x3 - 9y + 9x h) x2(x-1) + 16(1- x) n) 81x2 - 6yz - 9y2 - z2 m) xz-yz-x2+2xy-y2 p) x2 + 8x + 15 k) 81x4 + 4

Đáp án+Giải thích các bước giải:

`2)` 

`a) (x + y)^2 - (x - y)^2=(x+y-x+y)(x+y+x-y)=2y.2x=4xy`

`b) (a + b)^3 + (a - b)^3 - 2a^3=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-2a^3=6ab^2`

`3)`

`a) x^2 - y^2 - 2x + 2y=(x^2-y^2)-(2x-2y)=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)`

`b) 2x + 2y - x^2 - xy=(2x+2y)-(x^2+xy)=2(x+y)-x(x+y)=(x+y)(2-x)`

`c) 3a^2 - 6ab + 3b^2 - 12c^2=3(a^2-2ab+b^2-4c^2)=3[(a^2-2ab+b^2)-4c^2]=3(a-b)^2-(2c)^2=3(a-b-2c)(a-b+2c)`

`d) x^2 - 25 + y^2 + 2xy=(x^2+2xy+y^2)-25=(x+y)^2-5^2=(x+y-5)(x+y+5)`

`e) a^2 + 2ab + b^2 - ac - bc=(a^2+2ab+b^2)-(ac+bc)=(a+b)^2-c(a+b)=(a+b)(a+b-c)`

`f) x^2 - 2x - 4y^2 - 4y=(x^2-4y^2)-(2x+4y)=(x-2y)(x+2y)-2(x+2y)=(x+2y)(x-2y-2)`

`g) x^2y - x^3 - 9y + 9x=(x^2y-x^3)-(9y-9x)=x^2(y-x)-9(y-x)=(y-x)(x^2-9)=(y-x)(x-3)(x+3)`

`h) x^2(x-1) + 16(1- x)=x^2(x-1)-16(x-1)=(x-1)(x^2-16)=(x-1)(x-4)(x+4)`

`n) 81x^2 - 6yz - 9y^2 - z^2=81x^2-(6yz+9y^2+z^2)=(9x)^2-(z+3y)^2=(9x-z-3y)(9x+z+3y)`

`m) xz-yz-x^2+2xy-y^2=(xz-yz)-(x^2-2xy+y^2)=z(x-y)-(x-y)^2=(x-y)(z-x+y)`

`p) x^2 + 8x + 15=x^2+3x+5x+15=(x^2+3x)+(5x+15)=x(x+3)+5(x+3)=(x+3)(x+5)`

`k)81x^4 + 4=(9x)^2+4-36x^2+36x^2=(9x^2+2-6x)(9x^2+2+6x)`