Question : If (a – b) = 1, what is the value of (a3 – b3)?
Option 1: a2 + ab + b2
Option 2: (a + b)2 + 3ab
Option 3: a2 – ab + b2
Option 4: a2 + 2ab + b2
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Correct Answer: a 2 + ab + b 2
Solution :
Given: a – b = 1
We know the algebraic identity, a
3
– b
3
= (a – b)(a
2
+ ab + b
2
)
Substitute the given value in the above formula and we get,
⇒ a
3
– b
3
= (1)(a
2
+ ab + b
2
)
So, a
3
– b
3
= a
2
+ ab + b
2
Hence, the correct answer is a
2
+ ab + b
2
.
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