An expression is shown below:

4(m + 3 + 5m)

part a: write two expressions that are equivalent to the given expression.

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.

part c: show that your other expression from part a is equivalent to the given expression by substituting a number for m.

Given Expression: 4 ( m + 3 + 5m )

Part A).

To find: Two Equivalent Expression to the given expression

1st Expression = 4m + 12 + 20m

2nd Expression = 4 ( 6m + 3 )

Part B).

To get 1st expression in part A i used Distributive property multiplication over addition.

a × ( b + c ) = a × b + a × c

Consider,

4 ( m + 3 + 5m )

Now,

4 × m + 4 × 3 + 4 × 5m

= 4m + 12 + 20m

Part C).

We need to show: 4 ( m + 3 + 5m ) = 4 ( 6m + 3 )

We show equal by putting m = 1

Consider,

LHS = 4 ( m + 3 + 5m ) = 4 ( 1 + 3 + 5 × 1 ) = 4 ( 1 + 3 + 5 ) = 4 × 9 = 36

RHS = 4 ( 6m + 5 ) = 4 ( 6 × 1 + 3 ) = 4 ( 6 + 3 ) = 4 × 9 = 36

So, LHS  = RHS

Hence Proved.

c: lkllmn.

hope it's you

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