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(x+3)(x+6) Answer

2 min read Jun 16, 2024
(x+3)(x+6) Answer

Expanding the Expression (x+3)(x+6)

This expression represents the product of two binomials: (x+3) and (x+6). To find the answer, we need to expand the expression using the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this to our expression:

  • Step 1: Distribute the first term of the first binomial (x) over the second binomial: x(x+6) = x² + 6x
  • Step 2: Distribute the second term of the first binomial (3) over the second binomial: 3(x+6) = 3x + 18
  • Step 3: Combine the results from steps 1 and 2: (x+3)(x+6) = x² + 6x + 3x + 18
  • Step 4: Simplify by combining like terms: (x+3)(x+6) = x² + 9x + 18

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps remember the order of multiplication when expanding two binomials.

  • F: Multiply the first terms of each binomial: x * x = x²
  • O: Multiply the outer terms: x * 6 = 6x
  • I: Multiply the inner terms: 3 * x = 3x
  • L: Multiply the last terms: 3 * 6 = 18
  • Combine: x² + 6x + 3x + 18 = x² + 9x + 18

Conclusion

Therefore, the expanded form of the expression (x+3)(x+6) is x² + 9x + 18. Both the distributive property and the FOIL method lead to the same answer.

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