Q. 3 E5.0( 1 Vote )

# Factorize the following expressions:25x2 + 4y2 + 9z2 – 20xy + 12yz – 30zx

Method 1

The above equation can be simplified as :
= (– 5x)2 + (2y)2 + (3z)2 + 2(– 5x)(2y) + 2(2y)(3z) + 2(3z)(– 5x)
This equation is of the form: p2 + q2 + r2 + 2pq + 2qr + 2rp

where p = – 5x, q = 2y, r = 3z
Using the identity: p2 + q2 + r2 + 2pq + 2qr + 2rp = (p + q + r)2
We get,
25x2 + 4y2 + 9z2 – 20xy + 12yz – 30zx = (– 5x + 2y + 3z)2

= (– 5x + 2y + 3z)2

= (– 1)2(5x – 2y – 3z)2

= (5x – 2y – 3z)2

Method 2

The above equation can be simplified as:

= (– 5x)2 + (2y)2 + (3z)2 + 2(– 5x)(2y) + 2(2y)(3z) + 2(3z)(– 5x)
= {
(– 5x)2 + 2(– 5x)(2y) + (2y)2} + (3z)2 + 2(2y)(3z) + 2(3z)(– 5x)
(
p2 + 2pq + q2 = (p + q)2)
= (– 5x + 2y)2 + (3z)2 + 2(2y)(3z) + 2(3z)(– 5x)
Taking 2(3z) common in term 2(2y)(3z) + 2(3z)(– 5x)
= (– 5x + 2y)2 + (3z)2 + 2(3z)(2y – 5x)
= (– 5x + 2y)2 + 2(3z)(2y – 5x) + (3z)2

This of the form: (p + q)2 + 2r(p + q) + r2

Where, p = – 5x, q = 2y and r = 3z

Using the identity: (p + q)2 = p2 + 2pq + q2

We get,

25x2 + 4y2 + 9z2 – 20xy + 12yz – 30zx = (– 5x + 2y + 3z)2

= (– 5x + 2y + 3z)2

= (– 1)2(5x – 2y – 3z)2

= (5x – 2y – 3z)2

25x2 + 4y2 + 9z2 – 20xy + 12yz – 30zx = (5x – 2y – 3z)2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 