Which of these expressions is equivalent to x^4–16?
(x^2+4)(x–2)(x+2)
(x^2–4)(x^2–4)
(x+2)(x–2)(x+2)(x–2)
(x^2–2)(x^2–2)
I know it is not B or D. But I am not sure if it is A or C.
Please help
Thank you, I figured out the answer was A, thank you for helping so much!(:
Yes, you should have figured it out because it was almost the same as the last one.
To determine which expression is equivalent to x^4–16, let's simplify each option step-by-step:
Option A: (x^2+4)(x–2)(x+2)
Start by multiplying the quadratic factors:
= (x^2+4)(x^2–4)
Next, apply the difference of squares identity to expand:
= [(x^2+2^2)(x^2–2^2)]
= [(x^2+4)(x^2–4)]
By comparing this simplified expression to the original one, x^4–16, we can see that this is indeed equivalent.
Option C: (x+2)(x–2)(x+2)(x–2)
Begin by multiplying the linear factors:
= (x^2–2^2)(x^2–2^2)
Again, apply the difference of squares identity:
= [(x^2–2)(x^2–2)]
This simplified expression is also equivalent to x^4–16.
Therefore, both options A and C are correct.
(x^2+4)(x^2-4)
= (x^2+4)(x-2)(x+2)