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Expanding (x + 6)(x + 6)
This expression represents the product of two identical binomials: (x + 6) and (x + 6). We can expand it using the FOIL method (First, Outer, Inner, Last) or by applying the distributive property.
1. Using the FOIL Method
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 6 = 6x
- Inner: Multiply the inner terms of the binomials: 6 * x = 6x
- Last: Multiply the last terms of each binomial: 6 * 6 = 36
Now, combine the results: x² + 6x + 6x + 36
Finally, simplify by combining the like terms: x² + 12x + 36
2. Using the Distributive Property
- Distribute the first term of the first binomial (x) over the second binomial: x(x + 6) = x² + 6x
- Distribute the second term of the first binomial (6) over the second binomial: 6(x + 6) = 6x + 36
Now, combine the results: x² + 6x + 6x + 36
Finally, simplify by combining the like terms: x² + 12x + 36
Conclusion
Both methods lead to the same simplified expression: x² + 12x + 36. This is a perfect square trinomial, which is the result of squaring a binomial. In this case, it's the square of (x + 6).