SOLUTION: factor. x^3 + (x + 3)^3

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Question 1116301: factor.
x^3 + (x + 3)^3
Found 3 solutions by josgarithmetic, Edwin McCravy, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Look for the Sum Of Cubes formula.
Sums and Differences of Cubes - Purplemath Site
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Factor x³ + (x+3)³

Let y = x+3, then the above becomes:

x³ + y³

By the method for factoring the sum of two cubes,
the above becomes:

(x + y)(x² - xy + y²)

Change the parentheses to brackets

[x + y][x² - xy + y²]

Replace the y's by (x+3)

[x + (x+3)][x² - x(x+3) + (x+3)²]

[x + x + 3][x² - x² - 3x + (x+3)(x+3)]

[2x + 3][-3x + (x²+3x+3x+9)]

[2x + 3][-3x + (x²+6x+9)]

[2x + 3][-3x + x² + 6x + 9]

[2x + 3][x² + 3x + 9]

Change the brackets to parentheses:

(2x + 3)(x² + 3x + 9)

Edwin
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!

The best references on shortcut cubic multiplication formulas are these lessons

1. The cube of the sum formula is                 .
      For details and examples of applications of this formula see the lesson The cube of the sum formula


2. The cube of the difference formula is     .
      For details and examples of applications of this formula see the lesson The cube of the difference formula


3. The sum of cubes formula is                       .
      For details and examples of applications of this formula see the lesson The sum of cubes formula


4. The difference of cubes formula is           .
      For details and examples of applications of this formula see the lesson The difference of cubes formula



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