Question

Please help me. 50 points

An expression is shown below:

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

24m+12 is it simplified

Explanation:

A

2(12m+6)

12(2m+1)

B

Distributive property

2(12m+6) just has the 2 distributed out of 24m+12

Distributive Property again

12(2m+1) 12 was distributed out of 24m+12

Distributive property a ( b + c ) = a b + a c

C

say M is 2

4(2 + 3 + 5(2)) = 60

2(12(2)+6) = 60 as well (2x12 = 24, 24+6 = 30 times 2 is 60 )
2(12(2)+6) = 60 again (2 times 12 is 24+6 is 30, again 30x2=60 )

Answer 2

Expression 1: 4m+12+20m
Expression 2: 24m+12

Say that m=2 then the original expression would be 4(2+3+10) which is 60
Expression 1 would be 8+12+40 which also equals 60. The only difference between the two expressions is one used the distributive property.

For expression 2, m still equals 2 so it would be 48+12 which also equals 60 and for the this expression you used the distributive property and then addition.