Factor x^4-16

Problem

x^4−16

Solution

1. Identify the expression as a difference of squares, noting that x^4=(x^2)^2 and 16=4^2

2. Apply the formula for the difference of squares, a^2−b^2=(a−b)*(a+b) where a=x^2 and b=4

x^4−16=(x^2−4)*(x^2+4)

3. Identify that the first factor, x^2−4 is also a difference of squares because 4=2^2

4. Apply the formula again to the factor (x^2−4) using a=x and b=2

x^2−4=(x−2)*(x+2)

5. Combine all factors into the final expression, noting that x^2+4 cannot be factored further using real numbers.

(x−2)*(x+2)*(x^2+4)

Final Answer

x^4−16=(x−2)*(x+2)*(x^2+4)

Want more problems? Check here!