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Understanding (x + 9)(x + 9)
The expression (x + 9)(x + 9) represents the product of two binomials, both of which are identical: (x + 9). This type of multiplication is commonly referred to as squaring a binomial.
Expanding the Expression
To simplify this expression, we can use the FOIL method (First, Outer, Inner, Last):
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 9 = 9x
- Inner: Multiply the inner terms of the binomials: 9 * x = 9x
- Last: Multiply the last terms of each binomial: 9 * 9 = 81
Combining all the terms gives us: x² + 9x + 9x + 81
Finally, we combine the like terms: x² + 18x + 81
The Result: A Perfect Square Trinomial
The result, x² + 18x + 81, is a perfect square trinomial. This means that it can be factored back into the original binomial squared: (x + 9)².
Key Takeaways
- (x + 9)(x + 9) simplifies to x² + 18x + 81
- This expression represents a perfect square trinomial
- The FOIL method is a useful tool for expanding and simplifying expressions involving binomials.