%5E2.jpeg "(5m-2)^2")
Expanding and Simplifying (5m - 2)^2
The expression (5m - 2)^2 represents the square of a binomial, which is a polynomial with two terms. Expanding and simplifying this expression can be achieved using the following steps:
Understanding the Expression
(5m - 2)^2 is equivalent to multiplying the binomial (5m - 2) by itself. This can be written as:
(5m - 2) * (5m - 2)
Expanding the Expression
To expand the expression, we need to apply the distributive property. This means multiplying each term in the first binomial by each term in the second binomial.
- 5m * 5m = 25m^2
- 5m * -2 = -10m
- -2 * 5m = -10m
- -2 * -2 = 4
Combining Like Terms
After expanding, we can combine the like terms:
25m^2 - 10m - 10m + 4
This simplifies to:
25m^2 - 20m + 4
Final Result
Therefore, the expanded and simplified form of (5m - 2)^2 is 25m^2 - 20m + 4.
Important Note
It's crucial to remember that squaring a binomial does not simply involve squaring each term individually. We need to apply the distributive property to obtain the correct result.