Need Help With These Polynomials PLEASEE?

Question

#1. Multiply (6t - 5)(6t + 5)

#2. Multiply and Simplify (3n)^6 * (3n)^7


Need answers to check my own work. Thanks

Answer 1

#1. 36t^2 - 25. When you have a product of the form (a + b)(a - b), the result is a^2 - b^2.

#2. (3n)^13. When taking the product of two exponents with the same base, simply add the exponents.

Answer 2

#1. Multiply (6t - 5)(6t + 5)

(6t*5t) _ (6t*5) -(6t*5) - (5 * 5)
36t^2 -25



#2. Multiply and Simplify (3n)^6 * (3n)^7
Review rules of exponents... n is the same base, so your going to add exponents when you multiply.

(3*3)n^ (6+7)


9n^13

Answer 3

use FOIL for the first one
First 6t *6t
Outer 6t*5
Inner -5*6t
Last -5*5

Answer 4

1) Distribute the multiplication:
(This is the general rule for any polynomials).
(6t - 5)(6t + 5) =
6t (6t + 5) - 5(6t +5) =
36 t^2 + 30 t -30 t -25 =
36 t^2 - 25

In particular, the product of a sum of two numbers by the difference of the same two numbers, gives the difference of the squares:

a^2 - b^2 = (a+b)(a-b)

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An exponent shows how many times a number is multiplied by itself.

(3n)^6 = (3n)(3n)(3n)(3n)(3n)(3n)

Therefore
(3n)^6 * (3n)^7 =
(3n)(3n)(3n)(3n)(3n)(3n) * (3n)(3n)(3n)(3n)(3n)(3n)(3n) =
(3n)^13

In general, when multiplying powers of a same base (here, the base is 3n), you add the powers.

By the same approach, you can show yourself that for divisions, you subtract powers.

For example

(3n)^3 / (3n)^2 =
(3n)(3n)(3n) / (3n)(3n) =
(3n) * (3n)(3n)/(3n)(3n) =
(3n) * 1 = (3n)

or

(3n)^3 / (3n)^2 = (3n)^(3-2) = (3n)^1 = (3n)

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(3n)^6 / (3n)^7 =
(3n)(3n)(3n)(3n)(3n)(3n) / (3n)(3n)(3n)(3n)(3n)(3n)(3n) =
{(3n)(3n)(3n)(3n)(3n)(3n) / (3n)(3n)(3n)(3n)(3n)(3n)} * 1/(3n) =
1 * 1/(3n) = 1/(3n)
or
(3n)^6 / (3n)^7 = (3n)^(6-7) = (3n)^(-1)
Therefore
(3n)^(-1) = 1/(3n)

Negative powers mean fractions.

Answer 5

1.)(36t^2-25)
2.) (3^6)*(3^7)*(n^6)*(n^7)=(3^13)*n^13=(3n)^13