Question

Simplify

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

Answer 1

Answer:

Given:

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

2

−B

2

=(A−B)(A+B) ...1)

Now come to question:

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

2

−(1.5p−2.5q)

2

=4×(p+q)×(p−q)

This is answer.

Answer 2

Answer:

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

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

= will become ${(2.5p + 1.5q)}^{2} \: - \: {(1.5p \: - \: 2.5q)}^{2}$

Caz - - = +