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Select the two expressions that are equivalent to (3x + 5y)²

a. 9x² + 25y²
b. 3x² + 2(3x) (5y) + 5y²
c. (3x)² + 2(3x) (5y) + (5y)²
d. 3x)² + (3x) (5y) + (5y)²
e. 9x² + 30xy + 25y²

User Tam Huynh
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1 Answer

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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

User Dyaniyal Wilson
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