Question

Simplify fully please

Answer 1

Answer:

8x² + 8

Step-by-step explanation:

Given

(x² + 3)² - (x² - 1)² ← expand both factors using FOIL

= $x^{4}$ + 6x² + 9 - ($x^{4}$ - 2x² + 1) ← distribute by - 1

= $x^{4}$ + 6x² + 9 - $x^{4}$ + 2x² - 1 ← collect like terms

= 8x² + 8

Answer 2

Answer:

-8(x^2 - 1)

Step-by-step explanation:

(x^2 + 3)^2  and  (x^2 - 1)^2 are both squares of binomials.  The first step here is to expand both:

-(x^2 + 3)^2  =  -x^4 - 6x^2 - 9

(x^2 - 1)^2     =  x^4 - 2x^2 + 1

Combine the two right-hand expressions, obtaining:

-8x^2 - 8 or -8(x^2 - 1)

This -8(x^2 - 1) is the simplest form of the given expression.

If desired, -8(x^2 - 1)  can be factored:   -8(x - 1)(x + 1)