(4x-1).jpeg "(4x+1)(4x-1)")
Expanding the Expression: (4x + 1)(4x - 1)
This expression represents the product of two binomials. We can expand it using the FOIL method (First, Outer, Inner, Last) or by recognizing the pattern of a difference of squares.
Expanding using FOIL
FOIL stands for:
- First: Multiply the first terms of each binomial: (4x)(4x) = 16x²
- Outer: Multiply the outer terms: (4x)(-1) = -4x
- Inner: Multiply the inner terms: (1)(4x) = 4x
- Last: Multiply the last terms: (1)(-1) = -1
Now, combine the terms: 16x² - 4x + 4x - 1
Simplifying, we get: 16x² - 1
Difference of Squares
Notice that the expression (4x + 1)(4x - 1) fits the pattern of a difference of squares:
- (a + b)(a - b) = a² - b²
In this case, a = 4x and b = 1.
Applying the formula, we get: (4x)² - (1)² = 16x² - 1
Conclusion
Therefore, expanding the expression (4x + 1)(4x - 1) using either method results in the same simplified form: 16x² - 1. This demonstrates the power of recognizing patterns in algebra, which can make simplifying expressions much easier.