In factorization of perfect square trinomials we will
learn how to solve the algebraic expressions using the formulas.** **To factorize an algebraic expression
expressible as a perfect square, we use the following identities:

(ii) a

**Note:** We will also learn to use two identities in the
same question, to factorize the expression.

Solved problems on factorization of perfect square trinomials:

**1. Factorization when the given expression
is a perfect square:**

We can express the given expression x4 - 10x

= (x

Now it’s in the form of the formula of a

= (x

= (x

We can express the given expression x

= (x)

Now we will apply the formula of a

= (x + 3)

= (x + 3) (x + 3)

We can express the given expression x

= (x

Now we will apply the formula of a

=(x

=(x

Now we will apply the formula of differences of two squares i.e. a

= (x + y) (x- y) (x + y) (x- y)

**2. Factorize using the identity: **

25 – x

= 25 - [x

Now we see that x

= (5)

Now we will apply the formula of differences of two squares i.e. a

= [5 + (x + y)] [5 - (x + y)]

= (5 + x + y) (5 – x - y)

1- 2xy- (x

= 1 - 2xy - x

= 1 - (x

= 1 - (x + y )

= (1)

= [1 + (x + y)] [1 - (x + y)]

= [1 + x + y] [1 - x - y]

**Note:**

We see that to solve the above problems on factorization of perfect square trinomials we not only used perfect square identities but we also used the difference of two squares identity in different situations.

**8th Grade Math Practice**

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