Factor 12t^8-75t^4

Problem

12*t8−75*t4

Solution

1. Identify the greatest common factor (GCF) of the two terms, which is 3*t4

2. Factor out the GCF from the expression.

3*t4*(4*t4−25)

3. Recognize that the expression inside the parentheses is a difference of squares, following the pattern a2−b2=(a−b)*(a+b)

4. Identify the terms for the difference of squares where a=2*t2 and b=5

5. Apply the formula for the difference of squares to factor the remaining binomial.

3*t4*(2*t2−5)*(2*t2+5)

Final Answer

12*t8−75*t4=3*t4*(2*t2−5)*(2*t2+5)

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