Using the difference of squares equation, a^2 - b^2 = (a - b) (a + b)a2−b2=(a−b)(a+b)
I can determine the answer based on the facts that x^8x8 can be formatted as a square, (x^4)^2(x4)2, and that 1 is a square (for itself). Because of these, I am able to use the difference of squares equation. I take the aa value, x^4x4, and take the bb value, 1, and plug them into the equation.
If we wanted to check this, we would need to expand the answer that we have gained using FOIL (First Outer Inner Last).
I will demonstrate the steps below:
(x^4 - 1)(x^4 + 1)(x4−1)(x4+1)
First:
x^8 = (x^4)(x^4)x8=(x4)(x4)
Outer:
x^4 = (x^4)(1)x4=(x4)(1)
Inner:
-x^4 = (x^4)(-1)−x4=(x4)(−1)
Last:
-1 = (-1)(1)−1=(−1)(1)
Final expanded form:
x^8 + x^4 - x^4 - 1x8+x4−x4−1
Which can then cancel the x^4x4 to get our original equation, confirming the answer is correct.
