Question

Factorise x^3-x=?... ​

Answer 1

STEP

1

:

Pulling out like terms

2.1 Pull out like factors :

x3 - x = x • (x2 - 1)

Trying to factor as a Difference of Squares:

2.2 Factoring: x2 - 1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x2 is the square of x1

• Factorization is : (x + 1) • (x - 1)

Answer 2

Factorisation

Factorisation is the process to make a single term.

We have been given an expression $\[x^3-x\]$ and we have been asked to factorise.

Let's start solving the expression and understanding the steps to get our final result.

$\Rightarrow x^3-x$

Bind the expressions with the common factor $x$;

$\Rightarrow x(x^2-1)$

Present as the shape of the power;

$\Rightarrow x(x^2-1^2)$

Organize by using $a^2 + b^2 = (a+b)(a-b)$;

$\Rightarrow x(x+1)(x-1)$

Now sort the factors;

$\Rightarrow \boxed{x(x-1)(x+1)}$

Hence, this is our required solution.

$\rule{90mm}{2pt}$

BRAINLY KNOWLEDGE

Factozisation : Factorizing is the process to make a single term. While factorising try to write everything as products (multiplication). For example:

$\Rightarrow 6x^2 - 9x + 10 = (2x - 5) (3x - 2)$

Step 1 : Find a common factor. For example:

$\Rightarrow 4xy + x^4 + x = x(4x + x^3 + 1)$

Step 2 : Count the number of terms. [terms are separated by + or -]

If none of these methods work, re-arrange the terms, or remove brackets and start again.