Công thức 1 : $(a+b)^2=a^2+2ab+b^2$

$VD:(x+y)^2=x^2+2xy+y^2$

$(x+2y)=x^2+4xy+4y^2$

$(2x+y)^2=4y^2+4xy+y^2$

Công thức 2 : $(a-b)^2=a^2-2ab+b^2$

$VD:(x-y)^2=x^2-2xy+y^2$

$(x-2y)^2=x^2-4xy+4y^2$

$(2x-y)^2=4y^2-4xy+y^2$

Công thức 3 : $a^2-b^2=(a-b)(a+b)$

$VD:x^2-y^2=(x-y)(x+y)$

$x^2-4=(x-2)(x+2)$

$y^2-9=(y-3)(y+3)$

Công thức 4 : $(a+b)^3=a^3+3a^2b+3ab^2+b^3$

$VD:(x+y)^3=x^3+3x^2y+3xy^2+y^3$

$(x+1)^3=x^3+3x^2y+3xy^2+1$

$(y+3)^3=y^3+9y^2+27y+27$

Công thức 5 : $(a-b)^3=a^3-3a^2b+3ab^2-b^3$

$VD:(x-y)^3=x^3-3x^2y+3xy^2-y^3$

$(x-1)^3=x^3-3x^2y+3xy^2-1$

$(y-3)^3=y^3-9y^2+27y-27$

Công thức 6 : $a^3+b^3=(a+b)(a^2+ab+b^2)$

$VD:x^3+y^3=(x+y)(x^2+xy+y^2)$

$y^3+4^3=(y+4)(y^2+4y+16)$

$x^3+(3y)^3=(x+3y)(x^2+3xy+9y^2)$

Công thức 7 : $a^3-b^3=(a-b)(a^2-ab+b^2)$

$VD:x^3-y^3=(x-y)(x^2-xy+y^2)$

$y^3-4^3=(y-4)(y^2-4y+16)$

$x^3-(3y)^3=(x-3y)(x^2-3xy+9y^2)$

HĐT số 1 : `(a+b)^2=a^2+2ab+b^2`

Vd :

`1)(x+2)^2=x^2+2.x.2+2^2=x^2+4x+4`

`2)(x+3)^2=x^2+2.x.3+3^2=x^2+6x+9`

`3)(2x+1)^2=(2x)^2+2.2x.1+1^2=4x^2+4x+1`

HĐT số 2 : `(a-b)^2=a^2-2ab+b^2`

Vd :

`1)(x-1)^2=x^2-2.x.1+1^2=x^2-2x+1`

`2)(x-3)^2=x^2-2.x.3+3^2=x^2-6x+9`

`3)(2x-3)^2=(2x)^2-2.2x.3-3^2=4x^2+12x+9`

HĐT số 3 : `a^2-b^2=(a+b)(a-b)`

Vd :

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

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

`3)x^2-16=x^2-4^2=(x-4)(x+4)`

HĐT số 4 : `a^3+b^3=(a+b)(a^2-ab+b^2)`

Vd :

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

`2)8x^3+8=(2x)^3+2^3=(2x+2)[(2x)^2-2x.2+2^2]=(2x+2)(4x^2-2x+4)`

`3)x^3+64=x^3+4^3=(x+4)(x^2-4x+16)`

HĐT số 5 : `a^3-b^3=(a-b)(a^2+ab+b^2)`

Vd :

`1)x^3-27=x^3-3^3=(x-3)(x^2+3x+9)`

`2)8x^3-64=(2x)^3-4^3=[(2x+4)[(2x)^2-2x.4+4^2]=(2x+2)(4x^2-8x+16)`

`3)x^3-64=x^3-4^3=(x-4)(x^2+4x+16)`

HĐT số 6 : `(a+b)^3=a^3+3a^2b+3ab^2+b^3`

Vd :

`1)(x+y)^3=x^3+3x^2y+3xy^2+y^3`

`2)(x+1)^3=x^3+3x^2+3x+1`

`3)(2x+1)^2=(2x)^3+3.(2x)^2.1+3.2x.1^2+1^3=8x^3+24x^2+6x+1`

HĐT số 7 : `(a-b)^3=a^3-3a^2b+3ab^2-b^3`

Vd :

`1)(x-y)^3=x^3-3x^2y+3xy^2-y^3`

`2)(x+2)^3=x^3+3x^2.2+3x.2^2+1=x^3-6x^2+12x-1`

`3)(2x+4)^2=(2x)^3+3.(2x)^2.4+3.2x.4^2+1^3=8x^3+48x^2+96x+64`