Factorise x^3+1/1/x^3 (i.e x cubed plus 1 and 1 over x cubed) how is it done? Thanks
I do not know what you mean
x^3 + 1/(1/x^3)
or what you said which is
x^3 + 1 + 1/x^3
????
if the first multiply top and bottom of second term by x^3
x^3 + x^3/1
= 2x^3
According to your wording,
(x^3 + 1) ÷ 1/x^3
which is
(x^3 + 1)(x^3)
= x^3(x+1)(x^2 - x + 1) , using the factoring of cubes principle
It Is Factorise x^3 + one whole number and a fraction 1/(x^3) just like e.g 1.5=1/1/2
To factorize the expression x^3 + 1 / (1 / x^3), we need to use a technique called the difference of cubes.
The difference of cubes formula states that for any two numbers a and b, the expression a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2).
Now, let's apply this formula to the given expression:
x^3 + 1 / (1 / x^3)
First, we can see that 1 / (1 / x^3) is equivalent to x^3. Therefore, the expression becomes:
x^3 + x^3
Now, we have two identical terms: x^3 + x^3. To factorize this, we can use the distributive property. We take out the common factor, which is x^3, and we get:
x^3(x^0 + 1)
Since any number to the power of 0 is equal to 1, x^0 simplifies to 1. Now, we have:
x^3(1 + 1)
Simplifying further, we get:
x^3(2)
Finally, we have the factored form:
2x^3
Therefore, the expression x^3 + 1 / (1 / x^3) can be factorized as 2x^3.
I hope this explanation helped you understand how to factorize this expression! Let me know if you have any further questions.