[tex]x^3-9x[/tex] is equivalent to the expression x(x + 3)(x – 3).
Solution:
Given expression:
[tex]x^3-9x[/tex]
To find the equivalent expression for the given expression.
[tex]x^3-9x[/tex]
Take the common term x outside.
[tex]x^3-9x=x(x^2-9)[/tex]
9 can be written as 3 × 3 = 3²
[tex]=x(x^2-3^2)[/tex]
Using the algebraic identity: [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]=x(x+3)(x-3)[/tex]
[tex]x^3-9x=x(x+3)(x-3)[/tex]
Hence [tex]x^3-9x[/tex] is equivalent to the expression x(x + 3)(x – 3).
Option A is the correct answer.
