Simplify the following problem using the distributive property: 4x + 6y + 3(x – y) – 5x. Show each step in your calculation and provide a reason why you can do each step. (Hint: You will use the number properties.) You will not get full credit if you do not give reasons.

Question

Simplify the following problem using the distributive property:  4x + 6y + 3(x – y) – 5x. Show each step in your calculation and provide a reason why you can do each step. (Hint: You will use the number properties.) You will not get full credit if you do not give reasons.

skullpatrol · Answer

Any ideas?
:-)

anonymous · Answer

no
thats why im asking

tkhunny · Answer

You probably should get started.  You'll probably have to get rid of the parentheses (properly) in order to combine those variables inside with those outside.

skullpatrol · Answer

Do you recall the distributive property?

anonymous · Answer

no

skullpatrol · Answer

$$\huge a(b+c)=?$$

anonymous · Answer

I mean, I've heard of it, just never used it

skullpatrol · Answer

Complete the above equation please.

skullpatrol · Answer

Are you still there?

anonymous · Answer

oh, yea sorry, my dad was wanting me

skullpatrol · Answer

Ok, np :-)

anonymous · Answer

my internet is about to go out

skullpatrol · Answer

$$\huge a(b+c) =?$$

skullpatrol · Answer

The distributive property is what is known as a property of real numbers. 

Which means it can not be proven, but instead is accepted as true. 

What it states is that the "a" can be "distributed" as a multiplier over the b and c.

skullpatrol · Answer

$$\Huge a(b+c)=ab+ac$$

skullpatrol · Answer

Note that this pattern also holds with respect to subtraction $$\large a(b-c)=ab-ac$$

skullpatrol · Answer

For your question:

Simplify the following problem using the distributive property:  $$\large 4x + 6y + 3(x – y)  -5x$$

Applying  the distributive property with respect to subtraction gives: $$\large 3(x-y) =3x-3y$$

skullpatrol · Answer

$$\large  4x + 6y + 3(x – y) -5x=4x+6y+3x-3y-5x$$

skullpatrol · Answer

Now use the definition of subtraction: $$\large a-b=a+(-b)$$  to replace the subtractions in your expression so far $$\large 4x+6y+3x-3y-5x = 4x+6y+3x+(-3y)+(-5x)$$

skullpatrol · Answer

The next step is to use the commutative property of addition: $$\large a+b=b+a$$  to rearrange the expression so that all the  terms with x in them such as 4x, 3x, and -5x are grouped together and the same for the terms with a y in them such as 6y and -3y. This will look like this: $$\large 4x+6y+3x+(-3y)+(-5x)=4x+3x+(-5x)+6y+(-3y)$$

skullpatrol · Answer

Next, use the distributive property in the other direction:  $$\large ba + ca = (b+c)a$$ $$\large (4+3-(5))x+(6+(-3))y = 2x+3y$$

anonymous · Answer

h