Factor 125x^3+64y^3

Problem

125*x^3+64*y^3

Solution

1. Identify the expression as a sum of two cubes, which follows the form a^3+b^3

2. Determine the cube roots of each term to find a and b

a=√(3,125*x^3)=5*x

b=√(3,64*y^3)=4*y

3. Apply the formula for the sum of cubes, which is a^3+b^3=(a+b)*(a^2−a*b+b^2)

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

(5*x+4*y)*((5*x)^2−(5*x)*(4*y)+(4*y)^2)

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

(5*x+4*y)*(25*x^2−20*x*y+16*y^2)

Final Answer

125*x^3+64*y^3=(5*x+4*y)*(25*x^2−20*x*y+16*y^2)

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