Question

PLS HELP ASAP!!

4(m + 3 + 5m)

Part A: Write two expressions that are equivalent to the given expression. (3 points)

Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)

Answer 1

Part A: 24m+12, 12(m+2)

Answer 2

See below.

Explanation:

Part A:

4(m + 3 + 5m) =

= 4m + 12 + 20m

4(m + 3 + 5m) =

= 4(6m + 3)

Part B:

Use the distributive property on the given expression to get the first expression.

4(m + 3 + 5m) =

= 4 * m + 4 * 3 + 4 * 5m

= 4m + 12 + 20m

Part C:

Let m = 2

a. Substitute 2 for m in the original expression:

4(m + 3 + 5m) =

= 4(2 + 3 + 5 * 2)

= 4(5 + 10)

= 4(15)

= 60

b. Substitute 2 for m in the second equivalent expression of part A.

4(6m + 3) =

= 4(6 * 2 + 3)

= 4(12 + 3)

= 4(15)

= 60

By substituting 2 for m, both expressions evaluate to 60.