9. $-5(y + 10)$
10. write $3x - 1 + 5x + 7$ in simplest form.
11. find $(x + 1) + (x + 1)$.
12. find $(4x - 7) - (2x - 2)$
find the gcf of each pair of monomials.
13. $3x$, $12x$
14. $16a$, $20ab$
15. $25cd$, $10d$

Question

Accepted Answer

### Problem 9: Simplify $-5(y + 10)$
# Explanation:
## Step 1: Apply the distributive property
The distributive property states that $a(b + c)=ab+ac$. Here, $a = - 5$, $b=y$ and $c = 10$. So we have $-5\times y+(-5)\times10$
## Step 2: Simplify the products
$-5\times y=-5y$ and $-5\times10=-50$. So the simplified form is $-5y - 50$
# Answer: $-5y-50$

### Problem 10: Write $3x-1 + 5x+7$ in simplest form
# Explanation:
## Step 1: Combine like terms (the $x$-terms)
The $x$-terms are $3x$ and $5x$. So $3x + 5x=(3 + 5)x=8x$
## Step 2: Combine the constant terms
The constant terms are $-1$ and $7$. So $-1+7 = 6$
## Step 3: Combine the results
Putting the two results together, we get $8x+6$
# Answer: $8x + 6$

### Problem 11: Find $(x + 1)+(x + 1)$
# Explanation:
## Step 1: Remove the parentheses
We have $x + 1+x + 1$
## Step 2: Combine like terms (the $x$-terms and the constant terms)
For the $x$-terms: $x+x=(1 + 1)x = 2x$
For the constant terms: $1+1=2$
## Step 3: Combine the results
Putting them together, we get $2x+2$
# Answer: $2x + 2$

### Problem 12: Find $(4x-7)-(2x - 2)$
# Explanation:
## Step 1: Remove the parentheses (distribute the negative sign)
$4x-7-2x + 2$ (because $-(2x-2)=-2x + 2$)
## Step 2: Combine like terms (the $x$-terms and the constant terms)
For the $x$-terms: $4x-2x=(4 - 2)x=2x$
For the constant terms: $-7 + 2=-5$
## Step 3: Combine the results
Putting them together, we get $2x-5$
# Answer: $2x-5$

### Problem 13: Find the GCF of $3x$ and $12x$
# Explanation:
## Step 1: Find the GCF of the coefficients
The coefficients are $3$ and $12$. The factors of $3$ are $1,3$ and the factors of $12$ are $1,2,3,4,6,12$. The greatest common factor of $3$ and $12$ is $3$
## Step 2: Find the GCF of the variable parts
The variable part of $3x$ is $x$ and the variable part of $12x$ is $x$. The GCF of $x$ and $x$ is $x$
## Step 3: Multiply the GCFs of the coefficients and variable parts
Multiply the GCF of the coefficients ($3$) and the GCF of the variable parts ($x$): $3\times x = 3x$
# Answer: $3x$

### Problem 14: Find the GCF of $16a$ and $20ab$
# Explanation:
## Step 1: Find the GCF of the coefficients
The coefficients are $16$ and $20$. The factors of $16$ are $1,2,4,8,16$ and the factors of $20$ are $1,2,4,5,10,20$. The greatest common factor of $16$ and $20$ is $4$
## Step 2: Find the GCF of the variable parts
The variable part of $16a$ is $a$ and the variable part of $20ab$ is $ab$. The GCF of $a$ and $ab$ is $a$ (since $a$ is a factor of $ab$)
## Step 3: Multiply the GCFs of the coefficients and variable parts
Multiply the GCF of the coefficients ($4$) and the GCF of the variable parts ($a$): $4\times a=4a$
# Answer: $4a$

### Problem 15: Find the GCF of $25cd$ and $10d$
# Explanation:
## Step 1: Find the GCF of the coefficients
The coefficients are $25$ and $10$. The factors of $25$ are $1,5,25$ and the factors of $10$ are $1,2,5,10$. The greatest common factor of $25$ and $10$ is $5$
## Step 2: Find the GCF of the variable parts
The variable part of $25cd$ is $cd$ and the variable part of $10d$ is $d$. The GCF of $cd$ and $d$ is $d$ (since $d$ is a factor of $cd$)
## Step 3: Multiply the GCFs of the coefficients and variable parts
Multiply the GCF of the coefficients ($5$) and the GCF of the variable parts ($d$): $5\times d = 5d$
# Answer: $5d$

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QUESTION IMAGE

Question

Explanation:

Problem 9: Simplify \(-5(y + 10)\)

Step 1: Apply the distributive property

Step 2: Simplify the products

Step 1: Combine like terms (the \(x\)-terms)

Step 2: Combine the constant terms

Step 3: Combine the results

Step 1: Remove the parentheses

Step 2: Combine like terms (the \(x\)-terms and the constant terms)

Step 3: Combine the results

Answer:

Problem 10: Write \(3x-1 + 5x+7\) in simplest form