Factorization involves representing an expression with smaller terms.
- When the greatest common factor is factored out, the equivalent expression is: [tex]3x^2(x^8 - 16)[/tex].
- The complete factored expression is: [tex]3x^2(x^4 - 4)(x^4 + 4)[/tex]
The expression is given as:
[tex]3x^{10} -48x^2[/tex]
The GCF of [tex]3x^{10}[/tex] and [tex]48x^2[/tex] is [tex]3x^2[/tex].
So, we have:
[tex]3x^{10} -48x^2 = 3x^2 \times x^8 - 3x^2 \times 16[/tex]
Factor out [tex]3x^2[/tex]
[tex]3x^{10} -48x^2 = 3x^2(x^8 - 16)[/tex]
To factorize the expression completely, we express [tex]x^8[/tex] and [tex]16[/tex] as squares.
So, we have:
[tex]3x^{10} -48x^2 = 3x^2((x^4)^2 - 4^2)[/tex]
Apply difference of two squares
[tex]3x^{10} -48x^2 = 3x^2(x^4 - 4)(x^4 + 4)[/tex]
So, the complete factor of [tex]3x^{10} -48x^2[/tex] is [tex]3x^2(x^4 - 4)(x^4 + 4)[/tex]
Read more about factorization at:
https://brainly.com/question/19386208
