Question

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

• A. $x^3-y^3$
• B. $x^3+y^3$
• C. $x^4+y^4$
• D. $x^4-y^4$

Answer 1

The correct option is D

$x^4-y^4$

$\text{To simplify :}(x+y)(x-y)(x^2+y^2)$

Using the identity,
$(a+b)(a-b)=a^2-b^2$

we get,
$(x+y)(x-y)(x^2+y^2)$
$=(x^2-y^2)(x^2+y^2)$

Using the same identity again,
$\text{where}a=x^2\text{and}b=y^2$,

we get,

$(x^2-y^2)(x^2+y^2)$
$={\left(x^2\right)}^2-{\left(y^2\right)}^2$
$=x^4-y^4$