Final answer:
The expression 15x+10y is factored by finding the greatest common factor, which is 5, resulting in the equivalent factored form of 5(3x + 2y). The check confirms that the factored form is correct.
Step-by-step explanation:
To match each expression written in standard form to the equivalent expression in factored form for the expression 15x+10y, we first look for common factors. In this case, both terms share a common factor of 5. By factoring out this greatest common factor, we simplify the expression as follows:
Original Expression: 15x + 10y
Factored Form: 5(3x + 2y)
To ensure we have the correct equivalent expression in factored form, we check by expanding the factored form to see if it gives us the original expression:
Check: 5(3x + 2y) = 15x + 10y
Since the expansion matches the original expression, our factored form of 5(3x + 2y) is reasonable and correct.