Express the expression below as a perfect square: a²+9b²+c²-6ab+6bc-2ac

Correct Answer is : (a−3b−c)2(a-3b-c)²(a−3b−c)2

Correct Answer is : (a−3b−c)2(a-3b-c)²(a−3b−c)2

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RRB ALP CBT I 25 Nov 2024 Shift 3 Paper

Question : 9 of 75

Marks: +1, -0

a^{2}+9b^{2}+c^{2}-6ab+6bc-2ac

Solution:

Concept:

Recognise the standard algebraic identity for the square of a trinomial:

(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

Explanation:

The given expression is

a^{2}+9b^{2}+c^{2}-6ab+6bc-2ac

Write

9b^{2}

(3b)^2

to identify the square terms:

a^2

(3b)^2

, and

c^2

Now match the product terms:

-6ab = 2(a)(-3b)

6bc = 2(-3b)(-c)

, and

-2ac = 2(a)(-c)

This fits the form

(x + y + z)^2

where

x = a

y = -3b

, and

z = -c

So the expression becomes

(a - 3b - c)^2

Thus, the given expression is a perfect square.

Answer:

Option C:

(a-3b-c)^2

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