(3x+5y)2-30xy=9x2+25y2

Jasonbradley

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Jun 16, 2024

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Expanding and Simplifying the Expression (3x + 5y)² - 30xy = 9x² + 25y²

This problem involves expanding a binomial squared and then simplifying the expression to see if it equals the given result. Let's break it down step-by-step:

Expanding the Binomial

The expression (3x + 5y)² represents the square of the binomial (3x + 5y). We can expand this using the following formula:

(a + b)² = a² + 2ab + b²

Applying this to our expression:

(3x + 5y)² = (3x)² + 2(3x)(5y) + (5y)² = 9x² + 30xy + 25y²

Simplifying the Entire Expression

Now let's substitute the expanded term back into the original expression:

(3x + 5y)² - 30xy = 9x² + 30xy + 25y² - 30xy

Notice that the terms +30xy and -30xy cancel each other out:

= 9x² + 25y²

Conclusion

Therefore, after expanding and simplifying, we find that the expression (3x + 5y)² - 30xy is indeed equal to 9x² + 25y².