In this article, we will cover 3 important algebraic identities with examples. Algebraic identities are following:

**1.**

**2.**

**3.**

Let's go through first algebraic identity.

.

It means that expression of the form is equal to .

Let's take an example, we have . Comparing with we get,

and .

By algebraic identity 1, we know that .

Therefore, .

Similarly, .

This is not just about expanding the expressions which are of the form but it is also about factorizing the polynomials which are of the form .

**GMAT Sample Problem 1:**

is equal to:

(A) (B)

(C) (D) None of the above

which is of the form .

By algebraic identity 1, we know that .

Therefore, .

Hence, the answer is** (B)**.

Now, we will cover sample problem regarding algebraic identity 2. According to algebraic identity 2, we have:

**GMAT Sample Problem 2:**

is equal to:

(A) (B)

(C) (D) None of the above

which is of the form .

By algebraic identity 2, we know that .

Therefore,

Hence, the answer is **(A)**.

Let's learn about 3rd algebraic identity now. According to 3rd algebraic identity we have:

.

**Example:**

**GMAT Sample Problem 3:**

is equal to:

(A) (B)

(C) (D) None of the above

which is of the form .

By algebraic identity 3, we know that .

Therefore, .

Hence, the answer is **(B)**.

Now we can try some complicated problems regarding these algebraic identities because they are important considering GMAT exam.

**GMAT Sample Problem 4:**

is equal to:

(A)

(B)

(C)

(D)

(E) None of the above

We can write expression as which is of the form .

By algebraic identity 3, we know that .

Therefore, **(1)**

Similarly, we have **(2)**

Putting equation **(2)** in equation **(1) **we get**,**

can be further expanded to .

Therefore,

Hence, the answer is **(C)**.

** GMAT Sample Problem 5:**

is equal to:

(A)

(B)

(C)

(D)

(E) None of the above

can be written as which is of the form .

By algebraic identity 1, we know that .

Therefore,

Hence, the answer is **(A)**.

**GMAT Sample Problem 6:**

is equal to:

(A)

(B)

(C)

(D) None of the above

can be written as which is of the form .

By algebraic identity 2, we know that .

Therefore,

Hence, the answer is **(B)**.

After good amount of practice, you would be able to answer similar problems by just looking at the choices. Let's try one more problem.

**GMAT Sample Problem 7:**

is equal to:

(A)

(B)

(C)

(D)

can be written as which is of the form

By algebraic identity 3, we know that

Therefore, ** (1)**

Similarly, we have ** (2)**

Putting equation **(2****)** in equation **(1)**, we get

Hence, the answer is **(C)**.