Question

Fartorise: 4x²-12ax-y²-z²-2yz+9a²

Answer 1

Hi there !!

Here's your answer

Given, to factorise
4x² - 12ax - y ² - z² -2yz + 9a²

Regrouping the terms,
We have,

(4x² - 12ax + 9a²) - (y² + 2yz + z² )

It can be seen that in (4x² - 12ax + 9a²), the 2nd identity ie, ( a - b)² = a² - 2ab+ b² will be used and in
(y² + 2yz + z² ) the first identity ie, (a+ b)² = a² + 2ab + b² can be used ,

So,

(2x)² - 2(2x)(3a) - (3a)² -((y)² + 2(y)(z) + (z)²


= (2x - 3a)² - (y + z)²
It can be seen that the terms 2x - 3a and y + z are operated by a negative sign,
Using the identity a² - b² = (a - b)(a +b) will be used where
a = 2x - 3a
b = y + z

We have,

(2x - 3a -(y + z))(2x - 3a +(y + z)

= ( 2z - 3a - y - z )(2x - 3a + y + z )
Is the answer