Question

x power 6 - y power 6 is equal to​

Answer 1

Step-by-step explanation:

x^6 - y^6 = (x^2 + y^2)[ (x^2+y^2)^2 - (3x^2.y^2)]

= (x^2+y^2)(x^4 + y^4) - (x^2 . y^2)(x^2+y^2)

= (x^3+y^3)(x-y)(x^2+Y^2+xy)

Answer 2

Solution:

$\longrightarrow\rm{x^6-y^6}$

$\longrightarrow$$\rm{(x^3)^2-(y^3)^2}$

Now, we are going to use an identity: $\rm{a^2-b^2 = (a+b)(a-b)}$ Let us use this identity:

$\longrightarrow$$\rm{(x^3+y^3)(x^3-y^3)}$

Further, we are going to use two more important identities:

• $\rm{(a^3+b^3) = (a+b)(a^2-ab+b^2)}$
• $\rm{(a^3-b^3) = (a-b)(a^2+ab+b^2)}$

Let us apply these two identities:

$\longrightarrow$$\rm{(x^3+y^3)(x^3-y^3) = (x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)}$

$\longrightarrow\rm{(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2)}$

Hence, your Question is factorized. From this, let us arrive the last statement for this problem:

$\longrightarrow\rm{x^6-y^6 = (x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2)}$