The expression (a + b − c)3 + (a &

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

The expression (a + b − c)³ + (a − b + c)³ − 8a³ is equal to:

Options:

6a(a − b + c)(c − a − b)

3a(a + b − c)(a − b + c)

6a(a + b − c)(a − b + c)

3a(a − b + c)(c − a − b)

Correct Answer:

6a(a − b + c)(c − a − b)

Explanation:

Let a = b = c = 1

(a + b – c)³ + (a – b + c)³ – 8a³ = 1 + 1 – 8 = (-6)

Checking option 3^rd.

6a(a – b + c) (c – a – b) = 6 × 1 × (-1) = (-6) Satisfied.

So the value of (a + b – c)³ + (a – b + c)³ – 8a³ = 6a(a – b + c) (c – a – b)