ANSWER TO QUESTION 1
[tex](3 {n}^{4} + 1) + ( - 8 {n}^{4} + 3) - ( - 8 {n}^{4} + 2)[/tex]
Let us expand the parenthesis first.
[tex](3 {n}^{4} + 1) + ( - 8 {n}^{4} + 3) - ( - 8 {n}^{4} + 2) = 3 {n}^{4} + 1 + - 8 {n}^{4} + 3 + 8 {n}^{4} - 2[/tex]
This will simplify to,
[tex](3 {n}^{4} + 1) + ( - 8 {n}^{4} + 3) - ( - 8 {n}^{4} + 2) = 3 {n}^{4} + 2[/tex]
ANSWER TO QUESTION 2
We want to write
[tex]6.5 \times 10 - 7[/tex]
in standard notation.
Let us simplify first to obtain,
[tex]6.5 \times 10 - 7 = 65 - 7[/tex]
[tex]6.5 \times 10 - 7 = 58[/tex]
In standard notation we have,
[tex]6.5 \times 10 - 7 = 5.8 \times {10}^{1} [/tex]
[tex]6.5 \times 10 - 7 = 5.8 \times {10}[/tex]
ANSWER TO QUESTION 3
This question requires us to write [tex](m-n)(m+n)[/tex] in words.
Subtract [tex]n[/tex]
from [tex]m[/tex]
and multiply the result by the sum of [tex]m[/tex]
and [tex]n[/tex].
ANSWER TO QUESTION 4
We want to simplify
[tex] ( - 3 {t}^{2} {u}^{3} )(5 {t}^{7} {u}^{8} ).[/tex]
We use the laws of exponents to simplify the above expression.
[tex] ( - 3 {t}^{2} {u}^{3} )(5 {t}^{7} {u}^{8} ) = - 3 \times 5 \times {t}^{2} \times {t}^{7} \times {u}^{3} \times {u}^{8} [/tex]
Recall that,
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
This implies that,
[tex] ( - 3 {t}^{2} {u}^{3} )(5 {t}^{7} {u}^{8} ) = - 15 \times {t}^{2 + 7} \times {u}^{3 + 8} [/tex]
This simplifies to,
[tex] ( - 3 {t}^{2} {u}^{3} )(5 {t}^{7} {u}^{8} ) = - 15 \times {t}^{9} \times {u}^{11} [/tex]
ANSWER TO QUESTION 5.
We want to complete the property of exponents given by,
[tex] {b}^{n} \times {b}^{m} [/tex]
According to this product property of exponents,since the bases are the same we write down one base and add the exponents to obtain,
[tex] {b}^{n} \times {b}^{m} = {b}^{m + n} [/tex]
ANSWER TO QUESTION 6.
Please see attachment for the long division
ANSWER TO QUESTION 7.
We were given the expression,
[tex]m(y) = \frac{2y + 5}{y - 7} [/tex]
This is a rational expression. The expression is not defined for
[tex]y = 7[/tex]
Therefore it is not possible to evaluate
[tex]m(7)[/tex]
Evaluating this will result in division by zero as shown below.
[tex]m(7) = \frac{2(7) + 5}{7 - 7} [/tex]
[tex]m(7) = \frac{19}{0} [/tex]
ANSWER TO QUESTION 8.
We want to factor the Greatest Common Factor out of
[tex]30 {t}^{2} u + 12t {u}^{2} + 24tu[/tex]
The greatest common factor is
[tex]6tu[/tex]
We factor it to obtain,
[tex]30 {t}^{2} u + 12t {u}^{2} + 24tu = 6tu(5t + 2u + 4)[/tex]
