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(x+1)(x+2)(x+3) Expand And Simplify

2 min read Jun 16, 2024
(x+1)(x+2)(x+3) Expand And Simplify

Expanding and Simplifying (x+1)(x+2)(x+3)

This article will guide you through the process of expanding and simplifying the expression (x+1)(x+2)(x+3).

Step 1: Expand the first two factors

First, we will expand the product of the first two factors, (x+1)(x+2):

(x+1)(x+2) = x(x+2) + 1(x+2) 
           = x² + 2x + x + 2
           = x² + 3x + 2

Step 2: Expand the result with the third factor

Now, we multiply the result (x² + 3x + 2) by the third factor (x+3):

(x² + 3x + 2)(x+3) = x²(x+3) + 3x(x+3) + 2(x+3)
                     = x³ + 3x² + 3x² + 9x + 2x + 6
                     = x³ + 6x² + 11x + 6

Final Result

Therefore, the expanded and simplified form of (x+1)(x+2)(x+3) is x³ + 6x² + 11x + 6.

Key Points to Remember

  • FOIL Method: You can use the FOIL method (First, Outer, Inner, Last) to expand two binomials.
  • Distributive Property: Remember to apply the distributive property when multiplying a polynomial by a binomial.
  • Combining Like Terms: Always combine like terms after each step to simplify the expression.

By following these steps, you can confidently expand and simplify any similar expression involving multiple factors.

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