Question

Factorize: (2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)² * ​

Answer 1

(2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)² = ( 3x + 4y ) ( 3x + 4y )

Given :

(2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)²

To find :

To factorise

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)²

Step 2 of 2 :

Factorise the expression

We are aware of the formula that

(a + b)² = a² + 2ab + b²

(2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)²

Let a = 2x + 3y & b = x + y

Then

(2x + 3y)² + 2(2x + 3y) (x + y) + (x + y)²

= a² + 2ab + b²

= (a + b)²

= ( 2x + 3y + x + y )²

= ( 3x + 4y )²

= ( 3x + 4y ) ( 3x + 4y )

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Solve the equation 12p-11=25

https://brainly.in/question/26811798

2. On common factorization 12a+9 becomes 3a(4a+3) 

https://brainly.in/question/30544360