Question

PLZ HELP ME!!!

Answer 1

Answer:

A: $6x^2(x^8-16)$

B: $6x^2(x^4+4)(x^2+2)(x^2-2)$

Step-by-step explanation:

A:

Our expression is $6x^{10}-96x^2$. We need to find some common factors. Clearly, we can see that both terms share the x² part, so we can definitely take that out:

$6x^{10}-96x^2$

$x^2(6x^8-96)$

Let's see if 96 is divisible by 6:

96 ÷ 6 = 16; since there's no remainder / the remainder is 0, we know 96 is divisible by 6, so we can also factor out 6:

$x^2(6x^8-96)$

$6x^2(x^8-16)$

Thus, the answer to part A is $6x^2(x^8-16)$.

B:

Look at the $x^8-16$ part of the above factored expression. Notice that it is a difference of squares (because $x^8=(x^4)^2$ and 16 = 4²), so we can write this as:

$x^8-16$

$(x^4+4)(x^4-4)$

Now take a look at the $(x^4-4)$ part. Again, it's a difference of squares because $x^4=(x^2)^2$ and 4 = 2², so rewrite that as:

$x^4-4$

$(x^2+2)(x^2-2)$

Put it all together:

$6x^2(x^4+4)(x^2+2)(x^2-2)$

Thus, the answer to part B is $6x^2(x^4+4)(x^2+2)(x^2-2)$.