$$x^2-y^2=(x-y)·(x+y)$$

$$x^3-y^3=(x-y)·(x^2+xy+y^2)$$

$$x^3+y^3=(x+y)·(x^2-xy+y^2)$$

$$x^4-y^4=(x-y)·(x+y)·(x^2+y^2)$$

$$x^5-y^5=(x-y)·(x^4+x^3·y+x^2·y^2+x·y^3+y^4)$$

$$x^5+y^5=(x-y)·(x^4-x^3·y+x^2·y^2-x·y^3+y^4)$$

$$x^6-y^6=(x-y)·(x+y)·(x^2+x·y+y^2)(x^2-x·y+y^2)$$

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

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

$$(x+y)^2=x^2+2·x·y+y^2$$

$$(x-y)^2=x^2-2·x·y+y^2$$

$$(x+y)^3=x^3+3·x^2·y+3·x·y^2+y^3$$

$$(x-y)^3=x^3-3·x^2·y+3·x·y^2-y^3$$

$$(x+y)^4=x^4+4·x^3·y+6·x^2·y^2+4·x·y^3+y^4$$

$$(x-y)^4=x^4-4·x^3·y+6·x^2·y^2-4·x·y^3+y^4$$

$$(x+y)^5=x^5+5·x^4·y+10·x^3·y^2+10·x^2·y^3+5·x·y^4+y^5$$

$$(x-y)^5=x^5-5·x^4·y+10·x^3·y^2-10·x^2·y^3+5·x·y^4-y^5$$

$$(x+y)^6=x^6+6·x^5·y+15·x^4·y^2+20·x^3·y^3+15·x^2·y^4+6·x·y^5+y^6$$

$$(x-y)^6=x^6-6·x^5·y+15·x^4·y^2-20·x^3·y^3+15·x^2·y^4-6·x·y^5+y^6$$