Question

Factorise the following: x
${x}^{2} + 4xy + 4 {y}^{2}$
x square + 4xy + 4y square​

Answer 1

Answer:

Step-by-step explanation:

x² + 4xy + 4y²

= (x)² + 2 ( x) ( 2y) + (2y)²

= ( x + 2y )² is the answer. ( ∵ (a + b)²=a²+2ab+b²)

Answer 2

Given:

$x^{2} + 4xy + 4 {y}^{2}$

To Find:

Factors of the given equation.

Solution:

The given equation can be written as,

$(x)^{2} + 2 \times (x )\times (2y )+ (2y)^{2}$

Let's assume,

$x = a \\ 2y = b$

so the equation will become,

$a^{2} + 2ab + b^{2}$

we know that ,

$(a + b)^{2} = a^{2} + 2ab + {b}^{2}$

when we put the values of a and b in the above equation will give,

$(x + 2y)^{2}$

this can be written as,

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

Hence, the factors of the given equation are,

Hence, the factors of the given equation are,$(x + 2y)(x + 2y)$