What is the expression in factored form? 9x^2 - 12x + 4

a. (3x + 2)^2

b. (-3x-2)^2

c. (3x-2)^2

d. (-3+2)(3x-2)

C. (3x - 2)²

Step-by-step explanation:

The square of a binomial can be written as (a + b)². If you expand this formula, you get

(a + b)(a + b). Use F.O.I.L. to multiply this out..

F - stands for 'Firsts' (the first values in each set of parenthesis)

O - stands for 'Outsides' ( the first value in the first set of parenthesis, and the  

second value in the second set of parenthesis)

I - stands for 'Insides' ( the second value in the first set of parenthesis, and  

the first value in the second set of parenthesis)

L - stands for 'Lasts' ( the second value in each set of parenthesis)

This is the order you multiply them in...so we get

F - a² (a times a)

O - ab  

I - ba (which we rewrite as ab, since order doesn't matter when multiplying)

L - b²

We add them together to get a² + ab + ab + b²

which simplifies to a² + 2ab + b²

Read this as, the square of the first term in the parenthesis (a²), plus twice the product of the terms (2ab is twice the product of a and b), plus the square of the last term in the parenthesis)

So to solve this we need to factor  9x² - 12x + 4

Look at the bold paragraph above and work backwards.  

Take the square root of the term 9x², which is 3x. That goes in the first value of the parenthesis, so we have

(3x + b)²  

We know that -12x is twice the product of the two terms, so we divide by 2 to see the product of the two terms.

-12x/2 = -6x,  

We know one term, so divide -6x by the first term, 3x, to find the second term.

-6x/3x = -2

So the last term in our set of parenthesis is -2, so we have

(3x - 2)²  

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

roots are from trees

step-by-step explanation: