Question

(1) m²-n² × m²+mn+n²
(m+n)² × m³- n³​

Answer 1

$\text { We have formula, } a^{2}-b^{2}=(a+b)(a-b)\\\text { And } a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\\\text { Now, } \frac{m^{2}-n^{2}}{(m+n)^{2}} \times \frac{m^{2}+m n+n^{2}}{m^{3}-n^{3}}$

$=\frac{(m+n)(m-n)}{(m+n)^{2}} \times \frac{\left(m^{2}+m n+n^{2}\right)}{(m-n)\left(m^{2}+m n+n^{2}\right)}$

$=\frac{1}{(m+n)}$

$\text { Hence, required answer is } \frac{1}{m+n}$