Question

x2+4x+8y+4xy+4y2, factorise it

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

We have to factorise x² + 4x + 8y + 4xy + 4y²

There are two variables in the given expression. let's try to arrange it in the proper format to solve this expression.

x² + 4x + 8y + 4xy + 4y²

= x² + 4xy + 4y² + 4x + 8y

= (x)² + 2(x)(2y) + (2y)² + 4(x + 2y)

we know, (a + b)² = a² + 2ab + b²

so, (x)² + 2(x)(2y) + (2y)² = (x + 2y)²

= (x + 2y)² + 4(x + 2y)

= (x + 2y)[(x + 2y) + 4]

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

Therefore the factors of x² + 4x + 8y + 4xy + 4y² are (x + 2y) and (x + 2y + 4)