Factor y^4-16

Problem

y^4−16

Solution

1. Identify the expression as a difference of squares, since y^4=(y^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=y^2 and b=4

y^4−16=(y^2−4)*(y^2+4)

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

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

y^2−4=(y−2)*(y+2)

5. Combine all factors into the final expression. Note that y^2+4 is a sum of squares and cannot be factored further using real numbers.

Final Answer

y^4−16=(y−2)*(y+2)*(y^2+4)

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