Question

Factorise the expression given below:

(36s2 - 164 t2) =

Answer 1

$\bf \: {36s}^{2} - {144t}^{2} = 36(s + 2t)(s - 2t)$

*Correct question is:

Given:

• A polynomial.
• $(36 {s}^{2} - 144 {t}^{2} )$

To find:

• Factorise the polynomial.

Solution:

Concept/identity to be used:

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

Step 1:

Simplify the given polynomial.

$( {6s)}^{2} - ( {12t)}^{2}$

Here,

One can compare the polynomial with identity written above.

$\bf x = 6s \\ \bf y = 12t$

Step 2:

Factorise the polynomial.

According to the identity, we can factorise the polynomial.

$( {6s)}^{2} - ( {12t)}^{2} = (6s + 12t)(6s - 12t)$

or, take 6 common from both factors,

$( {6s)}^{2} - ( {12t)}^{2} = 36(s + 2t)(s - 2t)$

Thus,

The factors of polynomial are $\bf {36s}^{2} - {144t}^{2} = 36(s + 2t)(s - 2t)$

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Answer 2

$\displaystyle \bf 36 {s}^{2} - \frac{1}{64} {t}^{2} = \bigg(6s + \frac{1}{8}t \bigg)\bigg(6s - \frac{1}{8}t \bigg)$

Correct question :

$\displaystyle \sf Factorise :\: \: 36 {s}^{2} - \frac{1}{64} {t}^{2}$

Given :

$\displaystyle \sf 36 {s}^{2} - \frac{1}{64} {t}^{2}$

To find :

To factorise the expression

Formula Used :

$\displaystyle \sf {a}^{2} - {b}^{2} = (a + b)(a - b)$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf 36 {s}^{2} - \frac{1}{64} {t}^{2}$

Step 2 of 2 :

Factorise the expression

$\displaystyle \sf 36 {s}^{2} - \frac{1}{64} {t}^{2}$

$\displaystyle \sf = 36 {s}^{2} - \frac{{t}^{2} }{64}$

$\displaystyle \sf = {(6s)}^{2} - { \bigg( \frac{t}{8} \bigg)}^{2}$

$\displaystyle \sf = \bigg(6s + \frac{t}{8}\bigg)\bigg(6s - \frac{t}{8}\bigg)\: \: \: \bigg[ \: \because \:{a}^{2} - {b}^{2} = (a + b)(a - b) \bigg]$

$\displaystyle \sf = \bigg(6s + \frac{1}{8}t \bigg)\bigg(6s - \frac{1}{8}t \bigg)$

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