Remove the brackets and simplify: $(a^{2} + b^{2} + 2 a b) - (a^{2} + b^{2} - 2 a b)$ .

Open in App

Solution

SImplifying the algebraic expression
Simplification rule: If there is a $" - "$ sign before a bracket, then the signs of all the terms inside the bracket changes but if there is a $“ + ”$ sign before the bracket, then no change of signs.
$\begin{array}{rcl} (a^{2} + b^{2} + 2 a b) - (a^{2} + b^{2} - 2 a b) & = & a^{2} + b^{2} + 2 a b - a^{2} - b^{2} + 2 a b \\ = & a^{2} - a^{2} + b^{2} - b^{2} + 2 a b + 2 a b \\ = & 4 a b \end{array}$
Therefore, the simplified expression is $4 a b$ .

Suggest Corrections

Similar questions

Q. Simplify:
(a² + b² + 2ab) − (a² + b² −2ab)

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

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

Q. Evaluate:

\sqrt{\frac{a^{2} + 2 a b + b^{2}}{a^{2} - 2 a b + b^{2}}}

Join BYJU'S Learning Program

Remove the brackets and simplify: (a2+b2+2ab)-(a2+b2-2ab).

Remove the brackets and simplify: $(a^{2} + b^{2} + 2 a b) - (a^{2} + b^{2} - 2 a b)$ .