Question

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

Answer 1

(3x+4y)²

Step-by-Step Explanation:

use square of sum: (a+b)²=a²+2ab+b².

(2x+3y+x+y)²

collect like terms

((2x+x)+(3y+y))²

simplify (2x+x)+(3y+y) to 3x + 4y

(3x+4y)²

Answer 2

`\tt {(3x + 4y)}^(2)`

Step-by-step explanation:

let (2x + 3y) be 'a'

and (x + y) be 'b'

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Then the equation will be

a² + 2ab + b²

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Opening the middle term

a² + ab + ab + b²

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Taking common multiple

a(a + b) +b(a + b)

(a + b)(a + b)

(a + b)²

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The real equation will be

(2x + 3y + x + y)²

(3x + 4y)²