Question

Applying a suitable identity find the product of (x - y), (x + y) and (x2 + y²).
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Answer 1

The product of (x - y)(x + y)($x^{2}$ + $y^{2}$) is

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

Step-by-step explanation:

We have,

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

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

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

[ ∵ (x - y)(x + y) = ($x^{2}$ - $y^{2}$)]

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

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

Hence, the product of (x - y)(x + y)($x^{2}$ + $y^{2}$) is

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

Answer 2

The product is  $(x-y)(x+y)(x^2+y^2)=x^4-y^4$

Step-by-step explanation:

To find : The product of $(x-y),(x+y)\text{ and }(x^2+y^2)$

Solution :

Write the expression as,

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

Applying identity, $(x-y)(x+y)=x^2-y^2$

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

Again apply the same identity with $x=x^2,y=y^2$

$=(x^2)^2-(y^2)^2$

$=x^4-y^4$

Therefore, $(x-y)(x+y)(x^2+y^2)=x^4-y^4$

#Learn more

Applying a suitable identity find the product of (x-y),(x+y) and (x²+y²)

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