Factor 64x^3+27y^3

Problem

64*x^3+27*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

3. Calculate a by taking the cube root of 64*x^3

a=4*x

4. Calculate b by taking the cube root of 27*y^3

b=3*y

5. Apply the formula for the sum of cubes: a^3+b^3=(a+b)*(a^2−a*b+b^2)

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

(4*x+3*y)*((4*x)^2−(4*x)*(3*y)+(3*y)^2)

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

(4*x+3*y)*(16*x^2−12*x*y+9*y^2)

Final Answer

64*x^3+27*y^3=(4*x+3*y)*(16*x^2−12*x*y+9*y^2)

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