Factorise the following : 25x² + 16y² + 4z² - 40xy + 16yz - 20xz
Solution:
Given, the expression is 25x² + 16y² + 4z² - 40xy + 16yz - 20xz ---- (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 = 25x²
a = 5x
b² = 16y²
b = 4y
c² = 4z²
c = 2z
2ab = - 40xy
ab = -20xy
a(4y) = -20xy
a = -20xy/4y
a = -5x
2bc = +16yz
bc = 8yz
2ca = -20xz
ca = -10xz
(2z)a = -10xz
a = -10xz/2z
a = -5x
So, a = -5x; b = 4y and c = 2z
Now, (a + b + c)² = (-5x + 4y + 2z)²
Therefore, the factors of the given expression are (-5x + 4y + 2z) and (-5x + 4y + 2z)
✦ Try This: Factorise : 2x3 - 3x2 - 17x + 30.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 29(ii)
Factorise the following : 25x² + 16y² + 4z² - 40xy + 16yz - 20xz
Summary:
On facotirsing the expression 25x² + 16y² + 4z² - 40xy + 16yz - 20xz using the algebraic identity we get the factors as (-5x + 4y + 2z) and (-5x + 4y + 2z)
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