Question

Given the expression: 3x10 − 48x2

Answer 1

Factorization involves representing an expression with smaller terms.

• When the greatest common factor is factored out, the equivalent expression is: $3x^2(x^8 - 16)$.
• The complete factored expression is: $3x^2(x^4 - 4)(x^4 + 4)$

The expression is given as:

$3x^{10} -48x^2$

The GCF of $3x^{10}$ and $48x^2$ is $3x^2$.

So, we have:

$3x^{10} -48x^2 = 3x^2 \times x^8 - 3x^2 \times 16$

Factor out $3x^2$

$3x^{10} -48x^2 = 3x^2(x^8 - 16)$

To factorize the expression completely, we express $x^8$ and $16$ as squares.

So, we have:

$3x^{10} -48x^2 = 3x^2((x^4)^2 - 4^2)$

Apply difference of two squares

$3x^{10} -48x^2 = 3x^2(x^4 - 4)(x^4 + 4)$

So, the complete factor of $3x^{10} -48x^2$ is $3x^2(x^4 - 4)(x^4 + 4)$

Read more about factorization at:

brainly.com/question/19386208