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(4m+5n)2+(5m+4n)2

2 min read Jun 16, 2024
(4m+5n)2+(5m+4n)2

Expanding and Simplifying (4m + 5n)² + (5m + 4n)²

This expression involves squaring binomials and then adding the results. Let's break down the steps to simplify it:

1. Expanding the Squares

We use the FOIL method (First, Outer, Inner, Last) to expand the squares:

  • (4m + 5n)² = (4m + 5n)(4m + 5n)

    • First: 4m * 4m = 16m²
    • Outer: 4m * 5n = 20mn
    • Inner: 5n * 4m = 20mn
    • Last: 5n * 5n = 25n²
    • Combine like terms: 16m² + 20mn + 20mn + 25n² = 16m² + 40mn + 25n²

  • (5m + 4n)² = (5m + 4n)(5m + 4n)

    • First: 5m * 5m = 25m²
    • Outer: 5m * 4n = 20mn
    • Inner: 4n * 5m = 20mn
    • Last: 4n * 4n = 16n²
    • Combine like terms: 25m² + 20mn + 20mn + 16n² = 25m² + 40mn + 16n²

2. Combining the Results

Now we add the expanded expressions:

(16m² + 40mn + 25n²) + (25m² + 40mn + 16n²)

3. Simplifying

Combine like terms:

16m² + 25m² + 40mn + 40mn + 25n² + 16n² = 41m² + 80mn + 41n²

Final Result

Therefore, the simplified form of (4m + 5n)² + (5m + 4n)² is 41m² + 80mn + 41n².

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