Question

Simplify each of the following:

(i) (x+3)³ + (x−3)³

(ii) ${\left(\frac{x}{2}+\frac{y}{3}\right)}^3-{\left(\frac{x}{2}-\frac{y}{3}\right)}^3$

(iii) ${\left(x+\frac{2}{x}\right)}^3+{\left(x-\frac{2}{x}\right)}^3$

(iv) (2x − 5y)³ − (2x + 5y)³

Answer 1

In the given problem, we have to simplify equation

(i) Given

We shall use the identity

Here

By applying identity we get

Hence simplified form of expression is .

(ii) Given

We shall use the identity

Here

By applying identity we get

By rearranging the variable we get

Hence the simplified value of is

(iii) Given

We shall use the identity

Here

By applying identity we get

By rearranging the variable we get,

Hence the simplified value of is

(iv) Given

We shall use the identity

Here

By applying the identity we get

By rearranging the variable we get,

Hence the simplified value of is .