Question

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

Answer 1

QUESTION:

Simplify each expression

ANSWER:

1.)
`\green{{- 8n}}`

2.)
`\green{{- 2b - 60}}`

3.)
`\green{{- 10x - 14}}`

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
`\blue{{1}}` remains the same :

`\blue{{1}}`
`{× x = x}`

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of
`\blue{{1}}` and itself:

`{x = }`
`\blue{{1}}`
`{× x}`

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

`{x = 1x}`

This is why we can write the term without the coefficient as a term with coefficient
`{1}`

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}`

`\red{{1}}`
`{n -9n}`

Second, Collect like terms by subtracting their coefficients

`\red{{1n - 9n}}`

`\red{{( 1 - 9)n}}`

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}}`

`\red{{- (9 - 1)}}`

Subtract the numbers

- (
`\red{{9 - 1}}`)n

-
`\red{{8}}`n

`\green{\boxed{- 8n}}`

2.) First, Distribute - 6 through the parentheses

how?

Multiply each term in the parentheses by - 6

`\red{{- 6(b + 10)}}`

`\red{{- 6b - 6 × 10}}`

Multiply the numbers

-
`{6b}` -
`\red{{6 × 10}}`

-
`{6b}` -
`\red{{60}}`

Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

`\red{{- 6b + 4b}}`

`\red{{(- 6 + 4)b}}`

Calculate the sum

`\red{{(- 6 + 4)}}`b

`\red{{-2}}`b

`\green{\boxed{- 2b - 60}}`

3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

`\red{{2(x - 5)}}`

`\red{{2x - 2 × 5}}`

Multiply the numbers

`{2x -}`
`\red{{2 × 5}}`

`{2x -}`
`\red{{10}}`

Second, Distribute - 4 through the parentheses

how?

Multiply each term in the parentheses by - 4

`\red{{- 4(3x + 1)}}`

`\red{{- 4 × 3x - 4}}`

Calculate the product

-
`\red{{4 × 3}}`x - 4

-
`\red{{12}}`x - 4

Third, Collect like terms

how?

Collect like terms by subtracting their coefficient

`\red{{2x - 12x}}`

`\red{{(2 - 12)x}}`

Calculate the difference

`\red{{(2 - 12)}}`x

`\red{{- 10}}`x

Fourth, Calculate the difference

how?

Factor out the negative sign from the expression

`\red{{- 10 - 4}}`

`\red{{- (10 + 4)}}`

Add the numbers

- (
`\red{{10 + 4}}`)

-
`\red{{14}}`

`\green{\boxed{- 10x - 14}}`

That's all I know sorry but I hope it helps :)