Question

Factorise : x 2 + 4y 2 + 16z 2 +
4xy + 16yz +8zx

Answer 1

Answer:

here's ur answer

(x^2 +4y^2 + 16z^2)^2

(x^2+4y^2+16z^2)(x^2+4y^2+16z^2)

Step-by-step explanation:

Answer 2

$\sf {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 4xy + 16yz + 8zx = (x + 2y + 4z)(x + 2y + 4z)$

Given :

The expression

$\sf {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 4xy + 16yz + 8zx$

To find :

To factorise the expression

Formula :

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\sf {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 4xy + 16yz + 8zx$

Step 2 of 2 :

Factorise the expression

We use the formula ,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Thus we get

$\sf {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 4xy + 16yz + 8zx$

$\sf = {(x)}^{2} + {(2y)}^{2} + {(4z)}^{2} + 2.x.2y + 2.2y.4z + 2.x.4z$

$\sf = {(x + 2y + 4z)}^{2}$

$\sf = (x + 2y + 4z)(x + 2y + 4z)$