Question

Factorize using identities
4x^2+4x+1

Answer 1

Answer :

( 2x + 1 )²

Step-by-step explanation :

4x² + 4x + 1

On splitting the middle term ;

4x² + 2x + 2x + 1

⇒ 2x ( 2x + 1 ) + 1 ( 2x + 1 )

⇒ ( 2x + 1 ) ( 2x + 1 )

⇒ ( 2x + 1 )²

Hence, the answer is ( 2x + 1 )²

Let's check out the answer, by applying an identities ;

( a + b )² = a² + 2ab + b²

Here,

( 2x + 1 )² = (2x)² + 2 * 2x * 1 + (1)²

( 2x + 1 )² = 4x² + 4x + 1

Hence, the answer is ( 2x + 1 )²

Answer 2

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$\bold\green{solution}$ :-

=> 4x² + 4x + 1

=>4x² + 2x + 2x + 1

=> 2x ( 2x + 1 ) + 1 ( 2x + 1)

=> ( 2x + 1 ) ( 2x + 1 )

=> ( 2x + 1 )² Answer ✔

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