Question

Can someone help please

1. Add or subtract as indicated. Write the answer in descending order.
(3n4 + 1) + (–8n4 + 3) – (–8n4 + 2)

2. Write the number in standard notation: 6.5 × 10–7


3. Translate from algebraic form to English form.
(m – n)(m + n)

4. (–3t2u3)(5t7u8) = _______.

5. Complete the property of exponents. bn ⋅ bm = _______.

6. Divide the polynomials by using long division.
(x3 – x2 – 2x + 14) ÷ (x – 1)


7. Evaluate the rational function, if possible. m[y]=2y+5/y-7 , m[7]

8. Factor out the greatest common factor.
30t2u + 12tu2 + 24tu

Answer 1

ANSWER TO QUESTION 1


`(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2)`

Let us expand the parenthesis first.


`(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2) = 3 {n}^(4) + 1 + - 8 {n}^(4) + 3 + 8 {n}^(4) - 2`

This will simplify to,


`(3 {n}^(4) + 1) + ( - 8 {n}^(4) + 3) - ( - 8 {n}^(4) + 2) = 3 {n}^(4) + 2`

ANSWER TO QUESTION 2

We want to write

`6.5 * 10 - 7`

in standard notation.

Let us simplify first to obtain,


`6.5 * 10 - 7 = 65 - 7`


`6.5 * 10 - 7 = 58`

In standard notation we have,


`6.5 * 10 - 7 = 5.8 * {10}^(1)`


`6.5 * 10 - 7 = 5.8 * {10}`

ANSWER TO QUESTION 3

This question requires us to write
`(m-n)(m+n)` in words.

Subtract
`n`
from
`m`
and multiply the result by the sum of
`m`
and
`n`.

ANSWER TO QUESTION 4

We want to simplify


`( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ).`

We use the laws of exponents to simplify the above expression.


`( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 3 * 5 * {t}^(2) * {t}^(7) * {u}^(3) * {u}^(8)`

Recall that,


`{a}^(m) * {a}^(n) = {a}^(m + n)`

This implies that,


`( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 15 * {t}^(2 + 7) * {u}^(3 + 8)`

This simplifies to,


`( - 3 {t}^(2) {u}^(3) )(5 {t}^(7) {u}^(8) ) = - 15 * {t}^(9) * {u}^(11)`

ANSWER TO QUESTION 5.

We want to complete the property of exponents given by,


`{b}^(n) * {b}^(m)`

According to this product property of exponents,since the bases are the same we write down one base and add the exponents to obtain,


`{b}^(n) * {b}^(m) = {b}^(m + n)`

ANSWER TO QUESTION 6.



Please see attachment for the long division

ANSWER TO QUESTION 7.

We were given the expression,


`m(y) = (2y + 5)/(y - 7)`

This is a rational expression. The expression is not defined for

`y = 7`

Therefore it is not possible to evaluate

`m(7)`

Evaluating this will result in division by zero as shown below.


`m(7) = (2(7) + 5)/(7 - 7)`


`m(7) = (19)/(0)`
ANSWER TO QUESTION 8.

We want to factor the Greatest Common Factor out of

`30 {t}^(2) u + 12t {u}^(2) + 24tu`
The greatest common factor is

`6tu`

We factor it to obtain,


`30 {t}^(2) u + 12t {u}^(2) + 24tu = 6tu(5t + 2u + 4)`