Question

Factorise the following:-
9x^2 + 16y^2 + 4 - 24xy - 16y + 12x​

Answer 1

Given : 9x
2
+16y
2
+4z
2
−24xy+16yz−12xz

According to the equation,
(a+b+c)
2
=a
2
+b
2
+c
2
+2ab+2bc+2ca

So we get,
Using the formula we can it write it as

9x
2
+16y
2
+4z
2
−24xy+16yz−12xz=(−3x)
2
+(4y)
2
+(2z)
2
+2(−3x)(4y)+2(4y)(2z)+2(2z)(−3x)

On further calculation we get,

9x
2
+16y
2
+4z
2
−24xy+16yz−12xz=(−3x+4y+2z)
2


It can be written as

9x
2
+16y
2
+4z
2
−24xy+16yz−12xz=(−3x+4y+2z)(−3x+4y+2z)