Can someone help me with these and show the work also?

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 :)

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