Math / Algebra

Question $25 x-10 x y=$ $\square$ (Factor completely.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression $25x - 10xy$ by pulling out all the common factors from both terms. Watch out! Don't forget to factor out all common factors, both numbers and variables!

STEP 2

1. Find the Greatest Common Factor (GCF) of the coefficients.
2. Find the GCF of the variables.
3. Factor out the GCF.

STEP 3

Let's look at the coefficients of our terms, which are the numbers in front of the variables.
We have 25 and 10.
What's the biggest number that divides evenly into both of them?
It's 5!

STEP 4

Now, let's look at the variables.
We have an $x$ in both terms, $25x$ and $10xy$ .
So, $x$ is a common factor.
The first term has only $x$ and the second term has $xy$ .
Since the first term does not have a $y$ variable, $y$ is not a common factor.

STEP 5

We found that the GCF of the coefficients is 5 and the GCF of the variables is x.
This means the overall GCF of the terms $25x$ and $10xy$ is $\boldsymbol{5x}$ .
Let's factor it out:

STEP 6

We can rewrite $25x$ as $5x \cdot 5$ .
We're basically dividing $25x$ by $5x$ to get $5$ .
Remember, dividing by $5x$ and then multiplying by $5x$ is the same as multiplying by one, so we haven't changed the value of the expression.

STEP 7

Similarly, we can rewrite $10xy$ as $5x \cdot 2y$ .
We're dividing $10xy$ by $5x$ to get $2y$ .
Again, dividing by $5x$ and multiplying by $5x$ is the same as multiplying by one, so we're good.

STEP 8

Now, let's put it all together.
We have $25x - 10xy = (5x \cdot 5) - (5x \cdot 2y)$ .
We can factor out the $5x$ to get $5x(5 - 2y)$ .
Awesome!

STEP 9

The completely factored expression is $5x(5-2y)$ .

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Question $25 x-10 x y=$ $\square$ (Factor completely.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression $25x - 10xy$ by pulling out all the common factors from both terms. Watch out! Don't forget to factor out all common factors, both numbers and variables!

STEP 2

1. Find the Greatest Common Factor (GCF) of the coefficients.
2. Find the GCF of the variables.
3. Factor out the GCF.

STEP 3

Let's look at the coefficients of our terms, which are the numbers in front of the variables.
We have 25 and 10.
What's the biggest number that divides evenly into both of them?
It's 5!

STEP 4

Now, let's look at the variables.
We have an $x$ in both terms, $25x$ and $10xy$ .
So, $x$ is a common factor.
The first term has only $x$ and the second term has $xy$ .
Since the first term does not have a $y$ variable, $y$ is not a common factor.

STEP 5

We found that the GCF of the coefficients is 5 and the GCF of the variables is x.
This means the overall GCF of the terms $25x$ and $10xy$ is $\boldsymbol{5x}$ .
Let's factor it out:

STEP 6

We can rewrite $25x$ as $5x \cdot 5$ .
We're basically dividing $25x$ by $5x$ to get $5$ .
Remember, dividing by $5x$ and then multiplying by $5x$ is the same as multiplying by one, so we haven't changed the value of the expression.

STEP 7

Similarly, we can rewrite $10xy$ as $5x \cdot 2y$ .
We're dividing $10xy$ by $5x$ to get $2y$ .
Again, dividing by $5x$ and multiplying by $5x$ is the same as multiplying by one, so we're good.

STEP 8

Now, let's put it all together.
We have $25x - 10xy = (5x \cdot 5) - (5x \cdot 2y)$ .
We can factor out the $5x$ to get $5x(5 - 2y)$ .
Awesome!

STEP 9

The completely factored expression is $5x(5-2y)$ .

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Question25x−10xy=25 x-10 x y=25x−10xy= □\square□ (Factor completely.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression 25x−10xy25x - 10xy25x−10xy by pulling out all the **common factors** from both terms. Watch out! Don't forget to factor out *all* common factors, both numbers and variables!

STEP 2

1. Find the Greatest Common Factor (GCF) of the coefficients.2. Find the GCF of the variables.3. Factor out the GCF.

STEP 3

Let's look at the **coefficients** of our terms, which are the numbers in front of the variables.We have **25** and **10**.What's the biggest number that divides evenly into both of them?It's **5**!

STEP 4

Now, let's look at the **variables**.We have an xxx in both terms, 25x25x25x and 10xy10xy10xy.So, xxx is a common factor.The first term has only xxx and the second term has xyxyxy.Since the first term does *not* have a yyy variable, yyy is *not* a common factor.

STEP 5

We found that the **GCF of the coefficients** is **5** and the **GCF of the variables** is **x**.This means the **overall GCF** of the terms 25x25x25x and 10xy10xy10xy is 5x\boldsymbol{5x}5x.Let's **factor it out**:

STEP 6

We can rewrite 25x25x25x as 5x⋅55x \cdot 55x⋅5.We're basically dividing 25x25x25x by 5x5x5x to get 555.Remember, dividing by 5x5x5x and then multiplying by 5x5x5x is the same as multiplying by one, so we haven't changed the value of the expression.

STEP 7

Similarly, we can rewrite 10xy10xy10xy as 5x⋅2y5x \cdot 2y5x⋅2y.We're dividing 10xy10xy10xy by 5x5x5x to get 2y2y2y.Again, dividing by 5x5x5x and multiplying by 5x5x5x is the same as multiplying by one, so we're good.

STEP 8

Now, let's put it all together.We have 25x−10xy=(5x⋅5)−(5x⋅2y)25x - 10xy = (5x \cdot 5) - (5x \cdot 2y)25x−10xy=(5x⋅5)−(5x⋅2y).We can **factor out** the 5x5x5x to get 5x(5−2y)5x(5 - 2y)5x(5−2y).Awesome!

STEP 9

The completely factored expression is 5x(5−2y)5x(5-2y)5x(5−2y).

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Question $25 x-10 x y=$ $\square$ (Factor completely.)

What is this asking? We need to rewrite the expression $25x - 10xy$ by pulling out all the common factors from both terms. Watch out! Don't forget to factor out all common factors, both numbers and variables!

1. Find the Greatest Common Factor (GCF) of the coefficients.
2. Find the GCF of the variables.
3. Factor out the GCF.

Let's look at the coefficients of our terms, which are the numbers in front of the variables.
We have 25 and 10.
What's the biggest number that divides evenly into both of them?
It's 5!

Now, let's look at the variables.
We have an $x$ in both terms, $25x$ and $10xy$ .
So, $x$ is a common factor.
The first term has only $x$ and the second term has $xy$ .
Since the first term does not have a $y$ variable, $y$ is not a common factor.

We found that the GCF of the coefficients is 5 and the GCF of the variables is x.
This means the overall GCF of the terms $25x$ and $10xy$ is $\boldsymbol{5x}$ .
Let's factor it out:

We can rewrite $25x$ as $5x \cdot 5$ .
We're basically dividing $25x$ by $5x$ to get $5$ .
Remember, dividing by $5x$ and then multiplying by $5x$ is the same as multiplying by one, so we haven't changed the value of the expression.

Similarly, we can rewrite $10xy$ as $5x \cdot 2y$ .
We're dividing $10xy$ by $5x$ to get $2y$ .
Again, dividing by $5x$ and multiplying by $5x$ is the same as multiplying by one, so we're good.

Now, let's put it all together.
We have $25x - 10xy = (5x \cdot 5) - (5x \cdot 2y)$ .
We can factor out the $5x$ to get $5x(5 - 2y)$ .
Awesome!

The completely factored expression is $5x(5-2y)$ .