Math / Algebra

QuestionMatch the following expression with what it would be AFTER you distribute.
$6(x-3)$ $-6(x+3)$ $6(x+3)$ $-6(x-3)$ $6 x-18$ $6 x+18$ $-6 x+18$ $-6 x-18$

Studdy Solution

STEP 1

What is this asking? We need to rewrite each expression after distributing the number outside the parentheses. Watch out! Don't forget to distribute to both terms inside the parentheses, and be super careful with those negative signs!

STEP 2

1. Distribute the First Expression
2. Distribute the Second Expression
3. Distribute the Third Expression
4. Distribute the Fourth Expression

STEP 3

Alright, let's distribute $6(x-3)$ !
We're going to multiply the $6$ by both the $x$ and the $-3$ .

STEP 4

First, $6 \cdot x = 6x$ .

STEP 5

Next, $6 \cdot (-3) = -18$ .
Remember, a positive times a negative is a negative!

STEP 6

Putting it together, we get $6x - 18$ .
Boom!

STEP 7

Now, let's tackle $-6(x+3)$ .
We'll distribute the $-6$ to both terms inside.

STEP 8

$-6 \cdot x = -6x$ .

STEP 9

Then, $-6 \cdot 3 = -18$ .
Again, negative times positive equals negative.

STEP 10

So, we have $-6x - 18$ .
Fantastic!

STEP 11

Time for $6(x+3)$ .
Distribute that $6$ !

STEP 12

$6 \cdot x = 6x$ .

STEP 13

$6 \cdot 3 = 18$ .
Positive times positive is positive!

STEP 14

Combining gives us $6x + 18$ .
Keep it up!

STEP 15

Last one: $-6(x-3)$ .
Distribute the $-6$ .

STEP 16

$-6 \cdot x = -6x$ .

STEP 17

$-6 \cdot (-3) = 18$ .
Negative times negative is positive!
Don't forget that!

STEP 18

Putting it all together, we get $-6x + 18$ .
We did it!

STEP 19

$6(x-3)$ matches with $6x - 18$ . $-6(x+3)$ matches with $-6x - 18$ . $6(x+3)$ matches with $6x + 18$ . $-6(x-3)$ matches with $-6x + 18$ .

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QuestionMatch the following expression with what it would be AFTER you distribute.6(x−3)6(x-3)6(x−3) −6(x+3)-6(x+3)−6(x+3) 6(x+3)6(x+3)6(x+3) −6(x−3)-6(x-3)−6(x−3) 6x−186 x-186x−18 6x+186 x+186x+18 −6x+18-6 x+18−6x+18 −6x−18-6 x-18−6x−18

Studdy Solution

STEP 1

What is this asking? We need to rewrite each expression after distributing the number outside the parentheses. Watch out! Don't forget to distribute to *both* terms inside the parentheses, and be super careful with those negative signs!

STEP 2

1. Distribute the First Expression2. Distribute the Second Expression3. Distribute the Third Expression4. Distribute the Fourth Expression

STEP 3

Alright, let's **distribute** 6(x−3)6(x-3)6(x−3)!We're going to multiply the 666 by *both* the xxx and the −3-3−3.

STEP 4

First, 6⋅x=6x6 \cdot x = 6x6⋅x=6x.

STEP 5

Next, 6⋅(−3)=−186 \cdot (-3) = -186⋅(−3)=−18.Remember, a positive times a negative is a negative!

STEP 6

Putting it together, we get 6x−186x - 186x−18.Boom!

STEP 7

Now, let's tackle −6(x+3)-6(x+3)−6(x+3).We'll distribute the −6-6−6 to both terms inside.

STEP 8

−6⋅x=−6x-6 \cdot x = -6x−6⋅x=−6x.

STEP 9

Then, −6⋅3=−18-6 \cdot 3 = -18−6⋅3=−18.Again, negative times positive equals negative.

STEP 10

So, we have −6x−18-6x - 18−6x−18.Fantastic!

STEP 11

Time for 6(x+3)6(x+3)6(x+3).Distribute that 666!

STEP 12

6⋅x=6x6 \cdot x = 6x6⋅x=6x.

STEP 13

6⋅3=186 \cdot 3 = 186⋅3=18.Positive times positive is positive!

STEP 14

Combining gives us 6x+186x + 186x+18.Keep it up!

STEP 15

Last one: −6(x−3)-6(x-3)−6(x−3).Distribute the −6-6−6.

STEP 16

−6⋅x=−6x-6 \cdot x = -6x−6⋅x=−6x.

STEP 17

−6⋅(−3)=18-6 \cdot (-3) = 18−6⋅(−3)=18.Negative times negative is positive!Don't forget that!

STEP 18

Putting it all together, we get −6x+18-6x + 18−6x+18.We did it!

STEP 19

6(x−3)6(x-3)6(x−3) matches with 6x−186x - 186x−18. −6(x+3)-6(x+3)−6(x+3) matches with −6x−18-6x - 18−6x−18. 6(x+3)6(x+3)6(x+3) matches with 6x+186x + 186x+18. −6(x−3)-6(x-3)−6(x−3) matches with −6x+18-6x + 18−6x+18.

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QuestionMatch the following expression with what it would be AFTER you distribute.
$6(x-3)$ $-6(x+3)$ $6(x+3)$ $-6(x-3)$ $6 x-18$ $6 x+18$ $-6 x+18$ $-6 x-18$

What is this asking? We need to rewrite each expression after distributing the number outside the parentheses. Watch out! Don't forget to distribute to both terms inside the parentheses, and be super careful with those negative signs!

1. Distribute the First Expression
2. Distribute the Second Expression
3. Distribute the Third Expression
4. Distribute the Fourth Expression

Alright, let's distribute $6(x-3)$ !
We're going to multiply the $6$ by both the $x$ and the $-3$ .

First, $6 \cdot x = 6x$ .

Next, $6 \cdot (-3) = -18$ .
Remember, a positive times a negative is a negative!

Putting it together, we get $6x - 18$ .
Boom!

Now, let's tackle $-6(x+3)$ .
We'll distribute the $-6$ to both terms inside.

$-6 \cdot x = -6x$ .

Then, $-6 \cdot 3 = -18$ .
Again, negative times positive equals negative.

So, we have $-6x - 18$ .
Fantastic!

Time for $6(x+3)$ .
Distribute that $6$ !

$6 \cdot x = 6x$ .

$6 \cdot 3 = 18$ .
Positive times positive is positive!

Combining gives us $6x + 18$ .
Keep it up!

Last one: $-6(x-3)$ .
Distribute the $-6$ .

$-6 \cdot x = -6x$ .

$-6 \cdot (-3) = 18$ .
Negative times negative is positive!
Don't forget that!

Putting it all together, we get $-6x + 18$ .
We did it!

$6(x-3)$ matches with $6x - 18$ . $-6(x+3)$ matches with $-6x - 18$ . $6(x+3)$ matches with $6x + 18$ . $-6(x-3)$ matches with $-6x + 18$ .