Expand the following : (-x + 2y - 3z)²
Solution:
Given, the expression is (-x + 2y - 3z)²
We have to expand the expression.
Using the algebraic identity,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Here a = -x
b = 2y
c = -3z
On expanding the given expression,
(-x + 2y - 3z)² = (-x)² + (2y)² + (-3z)² + 2(-x)(2y) + 2(2y)(-3z) + 2(-3z)(-x)
= x² + 4y² + 9z² - 4xy - 12yz + 6zx
Therefore, (-x + 2y - 3z)² = x² + 4y² + 9z² - 4xy - 12yz + 6zx.
✦ Try This: Expand the following : (2a - 2b - c)²
Given, the expression is (2a - 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 = 2a
b = -2b
c = -c
On expanding the given expression,
(2a - 2b - c)² = (2a)² + (-2b)² + (-c)² + 2(2a)(-2b) + 2(-2b)(-c) + 2(-c)(2a)
= 4a² + 4b² + c² - 8ab + 4bc - 4ac
Therefore, (2a - 2b - c)² = 4a² + 4b² + c² - 8ab + 4bc - 4ac
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 28(iii)
Expand the following : (-x + 2y - 3z)²
Summary:
On expanding (-x + 2y - 3z)² using algebraic identity we get x² + 4y² + 9z² - 4xy - 12yz + 6zx
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