Question

Factorise the following.​

Answer 1

Given :-

81x⁴ - (1/81x⁴)

To find :-

The factorisation of the expression

Solution :-

Given expression is 81x⁴ - (1/81x⁴)

=> 9²(x²)² - [1/{9²(x²)²}]

=> (9x²)²-(1/(9x²)²

It is in the form of (a+b)(a-b)

Where a = 9x² and b = (1/9x²)

We know that

(a+b)(a-b) = a²-b²

=> [9x²+(1/9x²)][9x²-(1/9x²)]

=> [9x²+(1/9x²)][(3x)²-(1/3x)²]

[(3x)²-(1/3x)²] is in the form of (a+b)(a-b)

Where a = 3x and b = (1/3x)

We know that

(a+b)(a-b) = a²-b²

=> [9x²+(1/9x²)][3x+(1/3x)][3x-(1/3x)]

Answer :-

81x⁴-(1/81x⁴)=[9x²+(1/9x²)][3x+(1/3x)][3x-(1/3x)]

Used formulae:-

♦ (a+b)(a-b) = a²-b²

Answer 2

Answer:

Hope this will help u

Step-by-step explanation:

By using identity (a^2-b^2) we can solve this.