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Expanding and Simplifying the Expression (4m - 1)² + 8
This article will guide you through the process of expanding and simplifying the algebraic expression (4m - 1)² + 8.
Understanding the Expression
The expression involves the following:
- (4m - 1)²: This represents the square of the binomial (4m - 1). Squaring a binomial means multiplying it by itself.
- + 8: This is a constant term that will be added to the result of expanding (4m - 1)².
Expanding the Square
To expand (4m - 1)², we can use the FOIL method or the square of a binomial formula:
1. FOIL Method:
- First: 4m * 4m = 16m²
- Outer: 4m * -1 = -4m
- Inner: -1 * 4m = -4m
- Last: -1 * -1 = 1
Adding all the terms, we get: 16m² - 4m - 4m + 1
2. Square of a Binomial Formula:
(a - b)² = a² - 2ab + b²
Applying this formula to our expression:
(4m - 1)² = (4m)² - 2(4m)(1) + (1)² = 16m² - 8m + 1
Combining Terms
Now that we have expanded (4m - 1)², we can substitute it back into the original expression:
(4m - 1)² + 8 = 16m² - 8m + 1 + 8
Finally, we can combine the constant terms:
16m² - 8m + 9
Conclusion
Therefore, the simplified form of the expression (4m - 1)² + 8 is 16m² - 8m + 9.