Expand the following : (3a - 5b - c)²
Solution:
Given, the expression is (3a - 5b - c)²
We have to expand the expression.
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Here a = 3a
b = -5b
c = -c
On expanding the given expression,
(3a - 5b - c)² = (3a)² + (-5b)² + (-c)² + 2(3a)(-5b) + 2(-5b)(-c) + 2(-c)(3a)
= 9a² + 25b² + c² - 30ab + 10bc - 6ac
Therefore, (3a - 5b - c)² = 9a² + 25b² + c² - 30ab + 10bc - 6ac.
✦ Try This: Expand the following : (a - 2b - c)²
Given, the expression is (a - 2b - c)²
We have to expand the expression.
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Here a = a
b = -2b
c = -c
On expanding the given expression,
(a - 2b - c)² = (a)² + (-2b)² + (-c)² + 2(a)(-2b) + 2(-2b)(-c) + 2(-c)(a)
= a² + 4b² + c² - 4ab + 4bc - 2ac
Therefore, (a - 2b - c)² = a² + 4b² + c² - 4ab + 4bc - 2ac
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 28(ii)
Expand the following : (3a - 5b - c)²
Summary:
On expanding (3a - 5b - c)² using algebraic identity we get 9a² + 25b² + c² - 30ab + 10bc - 6ac
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