Factorise the following : 9x² + 4y² + 16z² + 12xy - 16yz - 24xz
Solution:
Given, the expression is 9x² + 4y² + 16z² + 12xy - 16yz - 24xz ---- (1)
We have to factorise the expression.
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca ---------- (2)
On comparing (1) and (2),
a² = 9x²
a = 3x
b² = 4y²
b = 2y
c² = 16z²
c = 4z
2ab = 12xy
ab = 6xy
2bc = -16yz
bc = -8yz
2y(c) = -8yz
c = -8yz/2y
c = -4z
2ca = -24xz
ca = -12xz
So, a = 3x; b = 2y and c = -4z
Now, (a + b + c)² = (3x + 2y - 4z)²
Therefore, the factors of the given expression are (3x + 2y - 4z) and (3x + 2y - 4z)
✦ Try This: Factorise (9x -1/5)2 - (x + 1/3)2.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 29(i)
Factorise the following : 9x² + 4y² + 16z² + 12xy - 16yz - 24xz
Summary:
On factorising the expression 9x² + 4y² + 16z² + 12xy - 16yz - 24xz using the algebraic identity we get the factors as (3x + 2y - 4z) and (3x + 2y - 4z)
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