In factorization of perfect square we will learn how to factor different types of algebraic expressions using the following identities.

(i) a(ii) a

Solved examples on factorization of perfect square:

**1.
Factorize the perfect
square completely:**

First we arrange the given expression 4x

4x

= (2x)

Now applying the formula of a

= (2x + 3y)

= (2x + 3y) (2x + 3y)

We can express the given expression 25x

= (5x)

Now we will apply the formula of a

= (5x – z)

= (5x – z)(5x – z)

**Solution:**

We can that the given expression is not a perfect square. To get the expression as a perfect square we need to add 1 at the same time subtract 1 to keep the expression unchanged.

= x= x

= [(x)

= (x + 3)

= (x + 3 + 1)(x + 3 - 1)

= (x + 4)(x + 2)

**2. Factor using the identity:**

4m

To get the above expression in the form of a

= 4m

= 4m

= (2m

Now we apply the formula of a

= (2m

= (2m

= (2m

= (2m

We see that the given expression (x + 2y)

Here, a = x + 2y and b = 3y – x

Now we will apply the formula of a

[(x + 2y) + (3y – x)]

= [x + 2y + 3y – x]

= [5y]

= 25y

**8th Grade Math Practice**

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