Factor 3x^4-48

Problem

3*x^4−48

Solution

1. Factor out the greatest common factor by identifying that both terms are divisible by 3

3*(x^4−16)

2. Identify the difference of squares within the parentheses, noting that x^4=(x^2)^2 and 16=4^2

3*((x^2)^2−4^2)

3. Apply the difference of squares formula a^2−b^2=(a−b)*(a+b) to the expression.

3*(x^2−4)*(x^2+4)

4. Factor the remaining difference of squares by recognizing that x^2−4 can be written as x^2−2^2

3*(x−2)*(x+2)*(x^2+4)

Final Answer

3*x^4−48=3*(x−2)*(x+2)*(x^2+4)

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