Question

simplify: (2.5p-1.5q)²-(1.5p-2.5q)²

Answer 1

Given:

$\mathbf{(2.5p-1.5q)^{2}-(1.5p-2.5q)^{2}}$

To Find:

Simplify above equation.

Solution:

We know the formula of identity formula:

$\mathbf{A^{2}-B^{2}=(A-B)(A+B)}$       ...1)

Now come to question:

$\mathbf{(2.5p-1.5q)^{2}-(1.5p-2.5q)^{2}}$      ...2)

On comparing the equation 1) and equation 2), we get:

A = 2.5 p - 1.5 q

and:

B = 1.5 p - 2.5 q

With help of equation 1):

$\mathbf{(2.5p-1.5q)^{2}-(1.5p-2.5q)^{2}=(2.5p-1.5q-1.5p+2.5q)(2.5p-1.5q+1.5p-2.5q)}$On simplify:

$\mathbf{(2.5p-1.5q)^{2}-(1.5p-2.5q)^{2}=(p+q)(4p-4q)}$

On taking 4 common in second bracket:

$\mathbf{(2.5p-1.5q)^{2}-(1.5p-2.5q)^{2}=4\times (p+q)\times (p-q)}$

This is answer.