QUESTION:
Simplify each expression
ANSWER:
1.) [tex]\green{{- 8n}}[/tex]
2.) [tex]\green{{- 2b - 60}}[/tex]
3.) [tex]\green{{- 10x - 14}}[/tex]
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 [tex]\blue{{1}}[/tex] remains the same :
[tex]\blue{{1}}[/tex] [tex]{× x = x}[/tex]
Step 1:
The equality can be read in the other way as a well, so any term can be written as a product of [tex]\blue{{1}}[/tex] and itself:
[tex]{x = }[/tex] [tex]\blue{{1}}[/tex] [tex]{× x}[/tex]
Step 2:
Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:
[tex]{x = 1x}[/tex]
This is why we can write the term without the coefficient as a term with coefficient [tex]{1}[/tex]
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
[tex]{n - 9n}[/tex]
[tex]\red{{1}}[/tex] [tex]{n -9n}[/tex]
Second, Collect like terms by subtracting their coefficients
[tex]\red{{1n - 9n}}[/tex]
[tex]\red{{( 1 - 9)n}}[/tex]
Third, Calculate the difference
how?
Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger
[tex]\red{{1 - 9}}[/tex]
[tex]\red{{- (9 - 1)}}[/tex]
Subtract the numbers
- ([tex]\red{{9 - 1}}[/tex])n
- [tex]\red{{8}}[/tex]n
[tex]\green{\boxed{- 8n}}[/tex]
2.) First, Distribute - 6 through the parentheses
how?
Multiply each term in the parentheses by - 6
[tex]\red{{- 6(b + 10)}}[/tex]
[tex]\red{{- 6b - 6 × 10}}[/tex]
Multiply the numbers
- [tex]{6b}[/tex] - [tex]\red{{6 × 10}}[/tex]
- [tex]{6b}[/tex] - [tex]\red{{60}}[/tex]
Second, Collect like term
how?
Collect like terms by calculating the sum or difference of their coefficient
[tex]\red{{- 6b + 4b}}[/tex]
[tex]\red{{(- 6 + 4)b}}[/tex]
Calculate the sum
[tex]\red{{(- 6 + 4)}}[/tex]b
[tex]\red{{-2}}[/tex]b
[tex]\green{\boxed{- 2b - 60}}[/tex]
3.) First, Distribute 2 through parentheses
how?
Multiply each term in the parentheses by 2
[tex]\red{{2(x - 5)}}[/tex]
[tex]\red{{2x - 2 × 5}}[/tex]
Multiply the numbers
[tex]{2x -}[/tex] [tex]\red{{2 × 5}}[/tex]
[tex]{2x -}[/tex] [tex]\red{{10}}[/tex]
Second, Distribute - 4 through the parentheses
how?
Multiply each term in the parentheses by - 4
[tex]\red{{- 4(3x + 1)}}[/tex]
[tex]\red{{- 4 × 3x - 4}}[/tex]
Calculate the product
- [tex]\red{{4 × 3}}[/tex]x - 4
- [tex]\red{{12}}[/tex]x - 4
Third, Collect like terms
how?
Collect like terms by subtracting their coefficient
[tex]\red{{2x - 12x}}[/tex]
[tex]\red{{(2 - 12)x}}[/tex]
Calculate the difference
[tex]\red{{(2 - 12)}}[/tex]x
[tex]\red{{- 10}}[/tex]x
Fourth, Calculate the difference
how?
Factor out the negative sign from the expression
[tex]\red{{- 10 - 4}}[/tex]
[tex]\red{{- (10 + 4)}}[/tex]
Add the numbers
- ([tex]\red{{10 + 4}}[/tex])
- [tex]\red{{14}}[/tex]
[tex]\green{\boxed{- 10x - 14}}[/tex]
That's all I know sorry but I hope it helps :)
