Factor 27s^3-125t^3

Problem

27*s3−125*t3

Solution

1. Identify the expression as a difference of two cubes, which follows the form a3−b3

2. Determine the values of a and b by taking the cube root of each term.

a=√(3,27*s3())=3*s()

b=√(3,125*t3)=5*t

3. Apply the formula for the difference of cubes: a3−b3=(a−b)*(a2+a*b+b2)

4. Substitute the values of a and b into the formula.

(3*s−5*t)*((3*s)2+(3*s)*(5*t)+(5*t)2)

5. Simplify the terms inside the second set of parentheses.

(3*s−5*t)*(9*s2+15*s(t)+25*t2)

Final Answer

27*s3−125*t3=(3*s−5*t)*(9*s2+15*s(t)+25*t2)

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