Question

factorise the following expressions using suitable identities


$a)100 - 9x {}^{2}$
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Answer 1

100-9x^2 can be written as 10^2 - 9x^2
It resembles the identity (a-b)^2 =(a+b)(a-b) . There you go, you can solve it easily then.

Answer 2

Answer :

Given :

a) 100 - 9x^2

Required to find :

1. Factorise the given expression

Solution :

To solve this type of questions you need to know about the different methods of factorisation and it is important to known what is meant by factorisation.

What is factorisation?

Factorisation is a method of expanding or reducing the given expression by using different methods.

Most polynomial expression can be factorise using various methods.

Various Methods of factorisation ?

Any given polynomial expression can be factorised in many ways.

Some of the methods are;

1. splitting the middle term
2. Factorising it using a identity
3. Factorising b diving it with a factor and Factorising the quotient.

These methods used in factorisation,

So, Now let's come to the question

The given polynomial expression is

$100 - 9 {x}^{2}$

For Factorising this expression we are going to use the 2nd method that is

Factorising using identity

The identity which we are going to use is

$(x {)}^{2} - (y {)}^{2} = (x + y)(x - y)$

So, using this expression we have to factorise the expression.

But before that we have to make some changes in it .

So it get matched with that formula.

Here is the complete solution ;

$100 - 9 {x}^{2} \\ = (10 {)}^{2} - (3x {)}^{2} \\ = using \: (x {)}^{2} - (y {)}^{2} = (x + y)(x - y) \\ = (10 + 3x)(10 - 3x)$

Hence,

The given polynomial expression is factorised.