%5E2.jpeg "(4m-5n)^2")
Expanding the Square: (4m - 5n)²
In mathematics, expanding squares is a common algebraic operation. Let's explore the process of expanding the expression (4m - 5n)².
Understanding the Concept
The expression (4m - 5n)² represents the square of a binomial, which means multiplying the binomial by itself:
(4m - 5n)² = (4m - 5n) * (4m - 5n)
Using the FOIL Method
To expand this, we can employ the FOIL method (First, Outer, Inner, Last):
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First: Multiply the first terms of each binomial: 4m * 4m = 16m²
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Outer: Multiply the outer terms: 4m * -5n = -20mn
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Inner: Multiply the inner terms: -5n * 4m = -20mn
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Last: Multiply the last terms: -5n * -5n = 25n²
Combining the Terms
Now, combine all the terms:
16m² - 20mn - 20mn + 25n²
Finally, simplify by combining the like terms:
16m² - 40mn + 25n²
Result
Therefore, the expanded form of (4m - 5n)² is 16m² - 40mn + 25n².