Question

Factorise completely .
49ײ-1/144
​

Answer 1

Answer:

(7x+12)(7x-12)

Step-by-step explanation:

This problem is known as a 'perfect square.' The square root of 49 is 7 and the square root of

x

2

is

x

. The next number, 144, is also a perfect square and the answer to that is 12.

Firstly, multiply the first numbers/variables: 7

x

⋅

7

x

=49

x

2

Secondly, multiply the outer numbers/vars.: 7

x

⋅

-12=-84

x

Thirdly, multiply the inner numbers/vars.: 7

x

⋅

12=84

x

Lastly, multiply the last numbers/vars.:12

⋅

12=144

The two number, 84

x

and 84

x

, cancel themselves out and leaves one with 49

x

-144

One CAN'T use this perfect square method IF the equation has a plus instead of a minus.

Answer 2

Answer:

[7x + (1/12)] [7x - (1/12)]

Step-by-step explanation:

$41 {x}^{2} - (1 \div 144)$

$= {(7x)}^{2} - {(1 \div 12)}^{2}$

Since,

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

Therefore,

[7x + (1/12)] × [7x - (1/12)]

(Sorry, I was actually using this latex maths for the first time)

Hope it helps