Ví dụ `1:`

`a) a^2-4b^2=a^2-(2b)^2=(a-2b)(a+2b)`

`b) 25a^2-1=(5a)^2-1^2=(5a-1)(5a+1)`

`c) a^2-9=a^2-3^2=(a-3)(a+3)`

`d),e)` bị khuyết `->` Xem lại đề.

`f) (2a+b)^2-a^2=[(2a+b)-a][(2a+b)+a]=(a+b)(3a+b)`

`g) 16(x-1)^2-25(x+y)^2=[4(x-1)]^2-[5(x+y)]^2=[4x-4-(5x+5y)][4x-4+(5x+5y)]=(-x-5y-4)(9x+5y-4)`

Ví dụ `2:`

`a) x^2+10x+25=x^2 +2.x.5+5^2=(x+5)^2`

`b) 25x^2-20xy+4y^2=(5x)^2 -2.5x.2y+(2y)^2=(5x-2y)^2`

`c) 9x^4+24x^2+16=(3x^2)^2+2 . 3x^2 . 4 + 4^2=(3x^2+4)^2`

`d) x^3+8=x^3+2^3=(x+2)(x^2-2x+4)`

`e) 8x^3+27y^3=(2x)^2+(3y)^3=(2x+3y)(4x^2-6xy+9y^2)`

`f) x^3-125=x^3-5^3=(x-5)(x^2+5x+25)`

`g) x^5-1=(x^3)^2-1^2=(x^3-1)(x^3+1)=(x-1)(x^2+x+1)(x+1)(x^2-x+1)`

`h) x^3+15x^2+75x+125=x^3 + 3 . x^2 . 5 + 3 . x . 5^2 + 5^3=(x+5)^3`

Ví dụ `1:`

`a) a(x-y)+bx-by`

`=a(x-y)+b(x-y)`

`=(x-y)(a+b)`

`b) 7a^2-7ax-9a+9x`

`=7a(a-x)-9(a-x)`

`=(a-x)(7a-9)`

`c) x^2+xy-2x-2y`

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

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

`d)2x^2-6xy+5x-15y`

`=2x(x-3y)+5(x-3y)`

`=(x-3y)(2x+5)`

`e)2ax^3+6ax^2+6ax+18a`

`=2a(x^3+3x^2+3x+9)`

`=2a[x^2(x+3)+3(x+3)]`

`=2a(x+3)(x^2+3)`

`f) ma-mb+na-nb-pa+pb`

`=m(a-b)+n(a-b)-p(a-b)`

`=(a-b)(m+n-p)`

`g) ax^2+5y-bx^2+ay+5x^2-by`

`=(ax^2-bx^2+5x^2)+(ay-by+5y)`

`=x^2(a-b+5)+y(a-b+5)`

`=(a-b+5)(x^2+y)`

`h)` Xem lại đề.

`i) a^3-b^3+3a^2+3ab+3b^2`

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

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

`j) a^4+a^3b-ab^3-b^4`

`=a^3(a+b)-b^3(a+b)`

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