Question

You can state the distributive property of multiplication over addition algebraically by using variables:

a. (b + c) = (a • b) + (a • c)
The distributive property tells you that a (b + c) and (a • b) + (a • c) are equivalent algebraic expressions.

1. Use the distributive property to write the following expression in an equivalent form: 3 • (5 + 25).
a) 90
b) 105
c) 120
d) 135

Answer 1

Using the distributive property, the expression 3 • (5 + 25) is equivalent to 90, after multiplying 3 by each term inside the parentheses and adding the results.

Step-by-step explanation:

The student has asked to use the distributive property of multiplication over addition to write the expression 3 • (5 + 25) in an equivalent form.

To apply the distributive property, we multiply the number outside the parentheses by each number inside the parentheses and then add the results together:

1. Multiply 3 by 5: 3 • 5 = 15.
2. Multiply 3 by 25: 3 • 25 = 75.
3. Add the results from steps 1 and 2 together: 15 + 75 = 90.

Therefore, using the distributive property, 3 • (5 + 25) is equivalent to 90, which corresponds to option (a).