Final answer:
The two expressions equivalent to (3x + 5y)² are (c) (3x)² + 2(3x)(5y) + (5y)² and (e) 9x² + 30xy + 25y².
Step-by-step explanation:
The question asks to select two expressions that are equivalent to (3x + 5y)². To find the correct expressions, we use the formula for squaring a binomial, which is (a + b)² = a² + 2ab + b². Applying this to our given expression:
(3x + 5y)² = (3x)² + 2(3x)(5y) + (5y)²
Calculating the squares and the product yields:
9x² + 30xy + 25y²
Thus, the equivalent expressions based on our original binomial squared are:
- (c) (3x)² + 2(3x)(5y) + (5y)²
- (e) 9x² + 30xy + 25y²