Question

Simplify-(x+y)(x-y)(x2+y2)​

Answer 1

Following are the steps for getting the answer :

Given:

(x+y)(x-y)(x²+y²)​

To find:

simplification of (x+y)(x-y)(x²+y²)​

Solution:

we have to simplify the (x+y)(x-y)(x²+y²)​

we know that,

(a+b)(a-b)=a²+b²

so, we can write this like,

=(x²+y²)(x²+y²)

Now multiply bracket 2 by bracket 1

we get,

=x²(x²+y²)+y²(x²+y²)

=$a^2+a^2=a^{2+2}=a^4$

$=x^{4} +x^2y^2+y^2x^2+y^4$

$=x^4+2x^2y^2+2x^2y^2+y^4\\\\=x^4+2x^2y^2+y^4$

we can write this

=(x²)²+2x²y²+(y²)²

we know that,

a²+2ab+b²=(a+b)²

so , (x²)²+2x²y²+(y²)²=(x+y)²

thus, the simplification of (x+y)(x-y)(x²+y²)​ is (x+y)²

Answer 2

Given equation is

$(x+y)(x-y)(x^{2} +y^{2} )$

Here we have to simplify the given equation

In the given equation the first two terms are in the form of a formula.

Formula:

$(a+b)(a-b)=a^{2} -b^{2}$

Here,

$a=x,b=y$

We can write this as,

$(x^{2} -y^{2})(x^{2} +y^{2} )$

Also the above equation is in the form of same formula.

Formula:

$(a+b)(a-b)=a^{2} -b^{2}$

Here,

$a=x^{2} ,b=y^{2}$

$(x^{2} )^{2} -(y^{2}) ^{2}$

$x^{4} -y^{4}$

Therefore, the final answer after simplification is $x^{4} -y^{4}$