Expand the following : (4a - b + 2c)²
Solution:
Given, the expression is (4a - b + 2c)²
We have to expand the expression.
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Here a = 4a
b = -b
c = 2c
On expanding the given expression,
(4a - b + 2c)² = (4a)² + (-b)² + (2c)² + 2(4a)(-b) + 2(-b)(2c) + 2(2c)(4a)
= 16a² + b² + 4c² - 8ab - 4bc + 16ac
Therefore, (4a - b + 2c)² = 16a² + b² + 4c² - 8ab - 4bc + 16ac
✦ Try This: Expand the following : (a - b - 2c)²
Given, the expression is (a - b - 2c)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 = -b
c = -2c
On expanding the given expression,
(a - b - 2c)² = (a)² + (-b)² + (-2c)² + 2(a)(-b) + 2(-b)(-2c) + 2(-2c)(a)
= a² + b² + 4c² - 2ab + 4bc - 4ac
Therefore, (a - b - 2c)² = a² + b² + 4c² - 2ab + 4bc - 4ac
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 28(i)
Expand the following : (4a - b + 2c)²
Summary:
On expanding (4a - b + 2c)² using algebraic identity we get 16a² + b² + 4c² - 8ab - 4bc + 16ac
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