Answer

Verified

421.2k+ views

**Hint:**

We first try to explain the concept of factorisation and the ways a factorisation of a polynomial can be done. We use the identity theorem of $ {{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) $ to factor the given polynomial $ 9{{x}^{2}}-25 $ . We assume the values of $ a=3x;b=5 $ . The final multiplied linear polynomials are the solution of the problem.

**Complete step by step answer:**

The main condition of factorization is to break the given number or function or polynomial into multiple of basic primary numbers or polynomials.

For the process of factorisation, we use the concept of common elements or identities to convert into multiplication form.

For the factorisation of the given quadratic polynomial $ 9{{x}^{2}}-25 $ , we apply the factorisation identity of difference of two squares as $ {{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) $ .

We get $ 9{{x}^{2}}-25={{\left( 3x \right)}^{2}}-{{5}^{2}} $ . We put the value of $ a=3x;b=5 $ .

Factorisation of the polynomial gives us

$ 9{{x}^{2}}-25={{\left( 3x \right)}^{2}}-{{5}^{2}}=\left( 3x+5 \right)\left( 3x-5 \right) $ .

These two multiplied linear polynomials can’t be broken anymore.

Therefore, the final factorisation of $ 9{{x}^{2}}-25 $ is $ \left( 3x+5 \right)\left( 3x-5 \right) $ .

**Note:**

The formula of $ {{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) $ derives from the solution identity of

\[\begin{align}

& {{a}^{2}}-{{b}^{2}} \\

& ={{a}^{2}}-ab+ab-{{b}^{2}} \\

& =a\left( a-b \right)+b\left( a-b \right) \\

& =\left( a+b \right)\left( a-b \right) \\

\end{align}\]

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How do you graph the function fx 4x class 9 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell