QUESTION:
Simplify each expression
ANSWER:
1.) ![\green{{- 8n}}](https://tex.z-dn.net/?f=%5Cgreen%7B%7B-%208n%7D%7D)
2.) ![\green{{- 2b - 60}}](https://tex.z-dn.net/?f=%5Cgreen%7B%7B-%202b%20-%2060%7D%7D)
3.) ![\green{{- 10x - 14}}](https://tex.z-dn.net/?f=%5Cgreen%7B%7B-%2010x%20-%2014%7D%7D)
4.) for number 4 study my step-by-step explanation so you can answer that
STEP-BY-STEP EXPLANATION:
1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1
WHY?
Learn why:
Why is it considered that the coefficient is 1?
Remember that any term multiplied by
remains the same :
![{× x = x}](https://tex.z-dn.net/?f=%7B%C3%97%20x%20%3D%20x%7D)
Step 1:
The equality can be read in the other way as a well, so any term can be written as a product of
and itself:
![{× x}](https://tex.z-dn.net/?f=%7B%C3%97%20x%7D)
Step 2:
Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:
![{x = 1x}](https://tex.z-dn.net/?f=%7Bx%20%3D%201x%7D)
This is why we can write the term without the coefficient as a term with coefficient ![{1}](https://tex.z-dn.net/?f=%7B1%7D)
Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1
![{n - 9n}](https://tex.z-dn.net/?f=%7Bn%20-%209n%7D)
![{n -9n}](https://tex.z-dn.net/?f=%7Bn%20-9n%7D)
Second, Collect like terms by subtracting their coefficients
![\red{{1n - 9n}}](https://tex.z-dn.net/?f=%5Cred%7B%7B1n%20-%209n%7D%7D)
![\red{{( 1 - 9)n}}](https://tex.z-dn.net/?f=%5Cred%7B%7B%28%201%20-%209%29n%7D%7D)
Third, Calculate the difference
how?
Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger
![\red{{1 - 9}}](https://tex.z-dn.net/?f=%5Cred%7B%7B1%20-%209%7D%7D)
![\red{{- (9 - 1)}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%20%289%20-%201%29%7D%7D)
Subtract the numbers
- (
)n
-
n
![\green{\boxed{- 8n}}](https://tex.z-dn.net/?f=%5Cgreen%7B%5Cboxed%7B-%208n%7D%7D)
2.) First, Distribute - 6 through the parentheses
how?
Multiply each term in the parentheses by - 6
![\red{{- 6(b + 10)}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%206%28b%20%2B%2010%29%7D%7D)
![\red{{- 6b - 6 × 10}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%206b%20-%206%20%C3%97%2010%7D%7D)
Multiply the numbers
-
- ![\red{{6 × 10}}](https://tex.z-dn.net/?f=%5Cred%7B%7B6%20%C3%97%2010%7D%7D)
-
- ![\red{{60}}](https://tex.z-dn.net/?f=%5Cred%7B%7B60%7D%7D)
Second, Collect like term
how?
Collect like terms by calculating the sum or difference of their coefficient
![\red{{- 6b + 4b}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%206b%20%2B%204b%7D%7D)
![\red{{(- 6 + 4)b}}](https://tex.z-dn.net/?f=%5Cred%7B%7B%28-%206%20%2B%204%29b%7D%7D)
Calculate the sum
b
b
![\green{\boxed{- 2b - 60}}](https://tex.z-dn.net/?f=%5Cgreen%7B%5Cboxed%7B-%202b%20-%2060%7D%7D)
3.) First, Distribute 2 through parentheses
how?
Multiply each term in the parentheses by 2
![\red{{2(x - 5)}}](https://tex.z-dn.net/?f=%5Cred%7B%7B2%28x%20-%205%29%7D%7D)
![\red{{2x - 2 × 5}}](https://tex.z-dn.net/?f=%5Cred%7B%7B2x%20-%202%20%C3%97%205%7D%7D)
Multiply the numbers
![\red{{2 × 5}}](https://tex.z-dn.net/?f=%5Cred%7B%7B2%20%C3%97%205%7D%7D)
![\red{{10}}](https://tex.z-dn.net/?f=%5Cred%7B%7B10%7D%7D)
Second, Distribute - 4 through the parentheses
how?
Multiply each term in the parentheses by - 4
![\red{{- 4(3x + 1)}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%204%283x%20%2B%201%29%7D%7D)
![\red{{- 4 × 3x - 4}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%204%20%C3%97%203x%20-%204%7D%7D)
Calculate the product
-
x - 4
-
x - 4
Third, Collect like terms
how?
Collect like terms by subtracting their coefficient
![\red{{2x - 12x}}](https://tex.z-dn.net/?f=%5Cred%7B%7B2x%20-%2012x%7D%7D)
![\red{{(2 - 12)x}}](https://tex.z-dn.net/?f=%5Cred%7B%7B%282%20-%2012%29x%7D%7D)
Calculate the difference
x
x
Fourth, Calculate the difference
how?
Factor out the negative sign from the expression
![\red{{- 10 - 4}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%2010%20-%204%7D%7D)
![\red{{- (10 + 4)}}](https://tex.z-dn.net/?f=%5Cred%7B%7B-%20%2810%20%2B%204%29%7D%7D)
Add the numbers
- (
)
- ![\red{{14}}](https://tex.z-dn.net/?f=%5Cred%7B%7B14%7D%7D)
![\green{\boxed{- 10x - 14}}](https://tex.z-dn.net/?f=%5Cgreen%7B%5Cboxed%7B-%2010x%20-%2014%7D%7D)
That's all I know sorry but I hope it helps :)