Question

4a²+ b²+4 ab +8a +4b+4​

Answer 1

Step-by-step explanation:

Factor each part separately:  

(2a)² + 4a(b + 2) + (b + 2)²  

Let u = 2a  

Let v = b + 2  

So you have:  

u² + 2uv + v²  

That's in the form of a perfect square:  

(u + v)²  

Answer

(2a + b+2)²

Answer 2

Factorise -

4a² + b² + 4ab + 8a + 4b + 4

Solution -

4a² + b² + 4ab + 8a + 4b + 4

=> 4a² + 4ab + b² + 8a + 4b + 4

=> ( 2a )² + 2 ( 2a )( b ) + b² + 8a + 4b + 4

=> ( 2a + b )² + 8a + 4b + 4

=> ( 2a + b )² + 4 ( 2a + b ) + 4 .

=> ( 2a + b )² + ( 2a + b ) [ 2 + 2 ] + 4

=> ( 2a + b )² + 2 ( 2a + b ) + 2 ( 2a + b ) + 4

=> ( 2a + b ) [ 2a + b + 2 ] + 2 ( 2a + b ) + 4

=> ( 2a + b ) [ 2a + b + 2 ] + 2 [ 2a + b + 2 ]

=> [ 2a + b + 2 ] ( 2a + b + 2 )

=> [ 2a + b + 2 ] × [ 2 a + b + 2 ]

=> [ 2a + b + 2 ]².

This is the required answer.

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