The value of $(a + b)^{2} - 2 (a - b)^{2} + (a - b) (a + b)$ is:

4 a b - b^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 a b - b^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 a b - b^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 a b - 2 b^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $6 a b - 2 b^{2}$
Given, $(a + b)^{2} - 2 (a - b)^{2} + (a - b) (a + b)$ .

We know, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ,
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
and $(a + b) (a - b) = a^{2} - b^{2}$ .

Then,
$(a + b)^{2} - 2 (a - b)^{2} + (a - b) (a + b)$
$= (a^{2} + b^{2} + 2 a b) - 2 (a^{2} + b^{2} - 2 a b) + (a^{2} - b^{2})$
$= a^{2} + b^{2} + 2 a b - 2 a^{2} - 2 b^{2} + 4 a b + a^{2} - b^{2}$
$= 2 a^{2} + b^{2} + 6 a b - 2 a^{2} - 3 b^{2}$
$= 6 a b - 2 b^{2}$ .

Therefore, option $D$ is correct.

Suggest Corrections

Similar questions

The factors of $8 a^{3} + b^{3} - 6 a b + 1$ are:

State True or False:

On subtracting $a^{2} + a b + b^{2}$ from $4 a^{2} - 3 a b + 2 b^{2}$ , the answer is $3 a^{2} - 4 a b + b^{2}$ .

Simplify $\frac{a - b}{a} + \frac{a + b}{b}$

Join BYJU'S Learning Program