Question

How do you factor $216 - {x^3}$.

Answer 1

Hint: This problem comes under factorisation of algebraic identities. First we need to know about algebra which is relations between variables and numerals. Here we factorise the given algebraic expression for that we need to know some identities of cubic expressions then by applying the identity then, we factorise the given expression with basic mathematical operation. Finally we get the required answer.

Formula used: Here we use this formula ${a^3} - {b^3} = (a - b)({a^2} + ab + {b^2})$ to apply and find the required answer.

Complete step-by-step solution:
It is given that the question stated as the expression $216 - {x^3}$
Here we have to convert the given expression as ${a^3} - {b^3}$, by applying this in the given expression, we can write it as
$ \Rightarrow {6^3} - {x^3}$
Now, we factorise the expression with the formula mentioned in formula used, we get
Here the values are $a = 6,b = x$,
Then we can write it as,
$ \Rightarrow {6^3} - {x^3} = (6 - x)({6^2} + 6x + {x^2})$
Now, simplifying square values, we get
$ \Rightarrow (6 - x)(36 + 6x + {x^2})$

Hence, we factorised the given expression, $(6 - x)(36 + 6x + {x^2})$ is the required answer.

Note: The formulas of algebraic expression and also for all mathematical expressions. This also can be said to evaluate the factors.
Factorisation is the product of factors in algebraic expression.
The polynomial of highest degree has three is called cubic polynomial. The basic thing in factorisation has been solving using identities.
Here we use cubic algebraic identities to find the factors of the expression. The cubic polynomial has been reduced which will become the formula itself.
In this we solve this by comparing the formula with expression and we evaluated it.