Algebra help 10 pts?

/
81x^2-9/121
-5+6/x^3

1) [ 9x + 3/11] [ 9x - 3/11]
= (9x)(9x) + (9x)(- 3/11) + (3/11)(9x) + (3/11)(-3/11)
= 81x^2 - (27/11)x + (27/11)x + 9/121
= 81x^2 + 9/121

2) (10x^8 - 12x^5) / -2x^8
= (10x^8/-2x^8) - (12x^5/-2x^8)
= -5 + 6/x^3

81x^2 - 9/121

1)
[9x + 3/11][9x - 3/11]
= 9x*9x + 3/11*9x - 9x*3/11 - 3/11*3/11
= 81x^2 + 27x/11 - 27x/11 - 9/121
= 81x^2 - 9/121

2)
(10x^8 - 12x^5)/(-2x^8)
= 2x^5(5x^3 - 6)/-2x^8
= (2/-2)(x^5/x^8)(5x^3 - 6)
= -1(1/x^3)(5x^3 - 6)
= -(5x^3 - 6)/x^3
= (-5x^3 + 6)/x^3
= -5x^3/x^3 + 6/x^3
= -5 + 6/x^3
= 6/x^3 - 5

Question 1
81x² - 9/121

If you mean :-
[ (9x + 3) / 11 ] [ (9x - 3) / 11 ]
(9x + 3)(9x - 3) / 121
(81x² - 9) / 121
9 (9x² - 1) / 121
9 (3x - 1)(3x + 1) / 121

Question 2
Suspect you may mean:-
(10x^8 - 12x^5) / (- 2x^8)
2x^5 (5x³ - 6) / (- 2x^8)
- (5x³ - 6) / x³
(6 - 5x³) / x³

1) FOIL(First Outer Inner Last):
[ 9x + 3/11] [ 9x - 3/11]
81x^2 - 27x/11 + 27x/11 - 9/121

81^2 - 9/121

2)
10x^8 - 12x^5
-------------------
-2x^8

It's easiest to go ahead and simplify the numbers because they are the easiest. So, go ahead and take out the -2:

6x^5 - 5x^8
---------------
x^8

Now, the rule for exponents: When you divide exponents, you subtract the bottom one from the top one. For example: (x^20)/(x^11) = x^9 :

6x^-3 - 5

Notice that you have a negative exponent. That means that the variable goes to the bottom(just the variable because only it is raised to a negative power, not the coefficient 6) :

6 - 5
--
x^3

Also, if you have something raised to a negative power and it is already in the denominator, bring it to the top. For instance: 1/(6^-2) = 36

I hope I helped!

1) [ 9x + 3/11] [ 9x - 3/11]
it is of the type (a + b)(a – b) = a² – b²
[ 9x + 3/11] [ 9x - 3/11]
= (9x)² – (3/11)²
= 81x² – 9/121
= [81x² × 121 – 9]/121
= [9801x² – 9]/121
= 9(1089x² – 1)/121

10x^8 - 12x^5 / -2x^8
= 5x^8 - 6x^5 / – x^8
= – 5x^8 + 6x^5 / x^8
= – 5x^(8 – 8) + 6x^(5–8)
= – 5 + 6x^(– 3)
= – 5 + 6/x³
= (6 – 5x³)/x³
----------

(9x)^2 - (3/11)^2
81x^2 - 9/121

1) apply (a+b)(a-b) formula
u get a`2 - b`2. so in the prob, the prodeuct is

81x`2 - 9/121
2)nd ques is not clear

1) (a+b)(a-b) = a^2 - a*b + b*a - b^2 = a^2 - b^2
so, 81x^2 - 9/121

2) (-12x^5) / (-2x^8) = 6/x^3
10x^8 + 6/x^3

If the expression was supposed to be:
(10x^8 - 12x^5)/(-2x^8)
then the answer becomes: -5 + 6/x^3