Question

# Which of the following is equivalent to the sum of the expressions a^{2} - 1 and a + 1 ?

- a
^{2} +a - a
^{3} - 1 - 2a
^{2} - a
^{3}

^{2}+a^{3}- 1^{2}^{3}## The correct answer is: a^{2} +a

### Solution:- (A) a^{2 }+ a

- Given two equations are a
^{2 }- 1 and a + 1.

Let A = a^{2 }– 1 and B = a + 1

- We have to find equivalent sum of both the expressions.
- Lets X be the sum of both the sums,

X = A + B

- Lets put the values of A and B in the equation

X = (a^{2 }– 1) + (a + 1)

X = a^{2 }– 1 + a + 1

- We can see that there are two terms -1 and 1, if we add both of them their sum will be 0.

X= a^{2 }+ a

- Therefore, the correct option is (A) a
^{2} + a

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