Factorise the following : 16x² + 4y² + 9z² - 16xy - 12yz + 24xz

Solution:

Given, the expression is 16x² + 4y² + 9z² - 16xy - 12yz + 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 = 16x²

a = 4x

b² = 4y²

b = 2y

c² = 9z²

c = 3z

2ab = - 16xy

ab = -8xy

(4x)b = -8xy

b = -8xy/4x

b = -2y

2bc = -12yz

bc = -6yz

b(3z) = -6yz

b = -6yz/3z

b = -2y

2ca = 24xz

ca = 12xz

So, a = 4x; b = -2y and c = 3z

Now, (a + b + c)² = (4x - 2y + 3z)²

Therefore, the factors of the given expression are (4x - 2y + 3z) and (4x - 2y + 3z)

✦ Try This: Factorise the following : 3x² + 4y² +25z²-4√3xy-20yz+10√3zx.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 29(iii)

Factorise the following : 16x² + 4y² + 9z² - 16xy - 12yz + 24xz

Summary:

On facotirsing the expression 16x² + 4y² + 9z² - 16xy - 12yz + 24xz using the algebraic identity we get the factors as (4x - 2y + 3z) and (4x - 2y + 3z)

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