Question

factorise x^4-81 using identity​

Answer 1

Answer:

x^4-81 = (x+3)(x-3)(x^2+9)

Step-by-step explanation:

We have (x^4-81). x^4 and 81 are both perfect squares, so we have the difference of 2 squares.

Identity

a^2 - b^2 = (a-b)(a+b)

we can write the equations in the power of 2

(x^2)^2 - 9^2

a = x^2

b = 9

x^4-81 = (x^2-9)(x^2+9)

as you can see (x^2-9) is also the difference of 2 squares so lets repeat the process

x^2

3^2

a = x

b = 3

x^2-9 = (x-3)(x+3)

now we can combine it all together

x^4-81 = (x+3)(x-3)(x^2+9)