Question

(2a-b)^2+(4a-2b)(a+b)+(a+b)^2​

Answer 1

Answer:

Expansion :-

9a²

Step-by-step explanation:

4a² + b² -4ab + 4a² - 2b² + 2ab + a² + b² + 2ab

9a² + 2b² - 2b² - 4ab + 4ab

= 9a²

Hope this helps

Answer 2

Step-by-step explanation:

Given:-

(2a-b)^2+(4a-2b)(a+b)+(a+b)^2

To find:-

Simplify the given expression?

Solution:-

Method-1:-

Given expression is

(2a-b)^2+(4a-2b)(a+b)+(a+b)^2

It can be written as

(2a-b)^2+2(2a-b)(a+b)+(a+b)^2

This is in the form of x^2+2xy +y^2

Where x = 2a-b and y = a+b

We know that

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

=>(2a-b)^2+2(2a-b)(a+b)+(a+b)^2

=>(2a-b+a+b)^2

=>(2a+a)^2

=>(3a)^2

=>3a×3a

=>9a^2

Method-2:-

Given expression is

(2a-b)^2+(4a-2b)(a+b)+(a+b)^2

=>[(2a)^2-2(2a)(b)+b^2]+[(4a)(a+b)-2b(a+b)]+[a^2+2ab+b^2]

=>(4a^2-4ab+b^2)+(4a^2+4ab-2ab-2b^2)+(a^2+2ab+b^2)

=>(4a^2+4a^2+a^2)+(-4ab+4ab-2ab+2ab)+(b^2-2b^2+b^2)

=>(9a^2)+(6ab-6ab)+(2b^2-2b^2)

=>9a^2+0+0

=>9a^2

Answer:-

The answer for the given problem is 9a^2

(2a-b)^2+(4a-2b)(a+b)+(a+b)^2 = 9a^2

Used formulae:-

• (x+y)^2 = x^2+2xy +y^2

• (x-y)^2 = x^2-2xy +y^2