%5E2---(3m-4)%5E2.jpeg "(5m-2)^2 - (3m-4)^2")
Factoring the Expression (5m-2)^2 - (3m-4)^2
This expression is a difference of squares, which can be factored using a specific formula. Here's how:
Understanding the Difference of Squares
The difference of squares formula states: a² - b² = (a + b)(a - b)
Applying the Formula
In our expression, we have:
- a = 5m - 2
- b = 3m - 4
Substituting these values into the difference of squares formula, we get:
(5m - 2)² - (3m - 4)² = [(5m - 2) + (3m - 4)][(5m - 2) - (3m - 4)]
Simplifying the Expression
Now, let's simplify the expression by combining like terms:
- [(5m - 2) + (3m - 4)] = 8m - 6
- [(5m - 2) - (3m - 4)] = 2m + 2
Therefore, the factored form of the expression is:
(8m - 6)(2m + 2)
Further Simplification
Notice that both terms in the factored expression have a common factor of 2. We can factor out this 2 to get the fully simplified expression:
2(4m - 3)(m + 1)
Conclusion
By applying the difference of squares formula and simplifying, we have successfully factored the expression (5m - 2)² - (3m - 4)² into its simplest form: 2(4m - 3)(m + 1).