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Expanding (x+8)(x+8)
The expression (x+8)(x+8) represents the product of two identical binomials. To simplify this expression, we can use the distributive property (also known as FOIL method) or a pattern recognition approach.
Using the Distributive Property (FOIL)
First: Multiply the first terms of each binomial.
- x * x = x²
Outer: Multiply the outer terms of the binomials.
- x * 8 = 8x
Inner: Multiply the inner terms of the binomials.
- 8 * x = 8x
Last: Multiply the last terms of each binomial.
- 8 * 8 = 64
Now, add all the terms together: x² + 8x + 8x + 64
Combine like terms: x² + 16x + 64
Recognizing the Pattern
The expression (x+8)(x+8) is actually a perfect square trinomial. This means it follows a specific pattern:
(a + b)² = a² + 2ab + b²
In our case, a = x and b = 8. Substituting these values into the pattern, we get:
x² + 2(x)(8) + 8²
Simplifying: x² + 16x + 64
Conclusion
Both methods lead to the same simplified expression: x² + 16x + 64. Understanding the pattern of perfect square trinomials can save time and effort when expanding similar expressions.