Question

Factorise 4x²+y²+4+4xy+4y+8x​

Answer 1

Formula:

(a + b)² = a² + 2ab + b²

Given expression,

4x² + y² + 4 + 4xy + 4y + 8x

after re-arranging expression becomes,

(2x)² + 4xy + y² + 8x + 4y + 4

= { (2x)² + 4xy + y² } + { 8x + 4y } + 4

= (2x + y)² + 4 (2x + y) + 4

= (2x + y)² + 2 × 2 × (2x + y) + 2²

= { (2x + y) + 2 }²

= ( 2x + y + 2 )²

Another method:

Formula:

(a + b + c)² = a²+b²+c²+2ab+2bc+2ac

Now, given expression,

4x² + y² + 4 + 4xy + 4y + 8x

After some modifications,

(2x)² + y² + 2² + 2(2x)(y) + 2(y)(2) + 2(2x)(2)

= (2x + y + 2)²