Equivalent expressions are expressions with equal values
The equivalent expression of [tex]\mathbf{x^6 - 16x^2}[/tex] is [tex]\mathbf{x^2(x + 2)(x - 2)(x^2 + 4)}[/tex]
The expression is given as:
[tex]\mathbf{x^6 - 16x^2}[/tex]
Factor out x^2
[tex]\mathbf{x^6 - 16x^2 = x^2(x^4 - 16)}[/tex]
Express x^4 as (x^2)^2
[tex]\mathbf{x^6 - 16x^2 = x^2((x^2)^2 - 16)}[/tex]
Express 16 as 4^2
[tex]\mathbf{x^6 - 16x^2 = x^2((x^2)^2 - 4^2)}[/tex]
Apply difference of two squares
[tex]\mathbf{x^6 - 16x^2 = x^2((x^2 - 4)(x^2 + 4))}[/tex]
Express 4 as 2^2
[tex]\mathbf{x^6 - 16x^2 = x^2((x^2 - 2^2)(x^2 + 4))}[/tex]
Apply difference of two squares
[tex]\mathbf{x^6 - 16x^2 = x^2(x + 2)(x - 2)(x^2 + 4)}[/tex]
Hence, the equivalent expression of [tex]\mathbf{x^6 - 16x^2}[/tex] is [tex]\mathbf{x^2(x + 2)(x - 2)(x^2 + 4)}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/15715866
