Question

Evaluate each of the following using identities:

(i) ${\left(2x-\frac{1}{x}\right)}^2$

(ii) (2x + y) (2x − y)

(iii) (a²b - b²a)²

(iv) (a - 0.1) (a + 0.1)

(v) (1.5x² − 0.3y²) (1.5x² + 0.3y²)

Answer 1

In the given problem, we have to evaluate expressions by using identities.

(i) Given

We shall use the identity

By applying identity we get

Hence the value of is

(ii) We have been given

We shall use the identity

Here,,

By applying identity we get

Hence the value ofis

(iii) The given expression is

We shall use the identity

Here

By applying identity we get

Hence the value of is

(iv) The given expression is $(a+0.1)(a-0.1)$

We shall use the identity

Here

By applying identity we get

$(a+0.1)(a-0.1)=a^2-{0.1}^2$

$=a^2-0.01$

Hence the value of $(a+0.1)(a-0.1)$ is

(v) The given expression is

We shall use the identity

Here

By applying identity we get

Hence the value ofis