Question

use a suitable identity to expand the following (p/8 -3q/10)² step by step​

Answer 1

Given: $(\frac{p}{8}-\frac{3q}{10})^{2}$

Here, We have to find the common denominator and solve,

$(\frac{p}{8}+\frac{-3q}{10})^{2}$

$(\frac{5p}{40}+\frac{4(-3)q}{40} )^{2}$

Now, combining the fraction with common denominator,

$(\frac{5p}{40}+\frac{4(-3)q}{40} )^{2}$

$(\frac{5p+4(-3)q}{40})^{2}$

Further, multiplying the numbers,

$(\frac{5p+4(-3)q}{40})^{2}$

We get,

$( \frac {5p - 12q} {40})^{2}$  is the final answer.

Answer 2

Using the identity $(x-y)^2=x^2+y^2-2xy$ :

$\left(\dfrac{p}{8} -\dfrac{3q}{10}\right)^2=\dfrac{p^2}{64} + \dfrac{9q^2}{100} - \dfrac{3qp}{40}$  

Given Expression is:

$\left(\dfrac{p}{8} -\dfrac{3q}{10}\right)^2$

To Find:

Expand Using Suitable Identity

Step 1 :

Identity to be used:

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

Step 2 :

Compare the Identity used and given expression

x = p/8

y = 3q/10

Step 3 :

Substitute the values in RHS of identity and simplify

$\left(\dfrac{p}{8}\right)^2 +\left(\dfrac{3q}{10}\right)^2-2\left(\dfrac{p}{8}\right)\left(\dfrac{3q}{10}\right)$

$=\dfrac{p^2}{64} + \dfrac{9q^2}{100} - \dfrac{3qp}{40}$

$\left(\dfrac{p}{8} -\dfrac{3q}{10}\right)^2=\dfrac{p^2}{64} + \dfrac{9q^2}{100} - \dfrac{3qp}{40}$