Help answer algebra problems(equations)?

Question

plz show steps if possible. answer any you can.
Factor each: 1) 3x(squared) + 21x 2) x(squared) -81 3) x(squared) + 12x + 35
Solve For x: 4) x(squared) - 7x - 30 = 0
Simplify: 36x(squred)y(squared) / 42xy(to third power)
and x(squared) - 2x - 35 / 42xy(to third power)
Solv for x: 4x / 54 = 2 / 3
Solve by substitution: {x = 2y - 3 and 3x + y = 5 }

Answer 1

1) 3x^2 + 21x
x(3x + 21)
3x(x + 7)
because of Distributive law
2) x^2 - 81
(x+9)(x-9)
because a^2 - b^2 = (a+b)(a-b)
3) x^2 + 12x + 35
first try to find 2 numbers that multiply to be 35. Then see which of those numbers add up to 12. 7*5 = 35 and 7+5 = 12. So, the answers are 5 and 7. They are both positive and so when in factor form, their signs must be negative. Thus, the factored form is: (x+5)(x+7)
or use the quadratic formula and get the same answer.
4) x^2 - 7x - 30 = 0
Use quadratic formula or the method I gave above-- find numbers that multiply to be -30 and from those that add to be 7. -2,15; 2,-15; -3,10; 3,-10; -1,30; 1,-30; -6,5; 6,-5 all multiply to be -30, but only -3, 10 add to be 7. So they are the answers. Now switch the signs and the 3 will be positive while the 10 is negative. Now add an x in front of each and put them in parentheses. Why should the sign be switched? Well in (x+3)(x-10), in order to find what one of the x's is, all we have to do is seperate that x from the equation and make it equal 0 like so: (x+3) = 0.Therefore x= -3. If it was (x-3) = 0, the answer would make x = 3.
So, the aswer is: (x+3)(x-10)
5) (36x^2*y^2)/(42x*y^3)
divide both numerator and denominator by 6.
(6x^2*y^2)/(7x*y^3)
which is basically (6*x*x*y*y)/(7*x*y*y*y)
so cross out the same variable on both sides since the coneection between them is multiplication
(6*x)/(7*y) is the answer
6) (x^2 - 2x - 35) / (42xy^3)
factor the top using the technique as written above, making the top factored into (x-7)(x+5)
so, the problem will be ((x-7)(x-5))/(42*x*y*y*y), which is the answer to itself
7) 4x/54 = 2/3
to get rid of 54 and keep the numbers to one side, multiply both sides by 54 and simplify the numerical side.
4x = 36
divide both sides by 4 to keep x by itself
x = 9
8) {x = 2y - 3 and 3x + y = 5 }
plug in 2y - 3 for x in the other equation. So, it's:
3(2y-3) + y =5
distribute:
6y - 9 + y = 5
simplify and get the variables to one side:
7y = 5 + 9
7y = 14
y = 2
I hope I was of help. Good luck further on. I hope I wasn't confusing

Answer 2

1) 3x (x+7)
2) (x+9) (x-9)
3) (x+7) (x+5)
4) (x+3) (x-10) => X= -3 or 10)
5) 6x/7y
6) (x+5) (x-7) / 42xy³
7) x = 9
8) if x = 2y -3 then 6y-9 +y = 5
7y - 9 = 5
7y = 14
y = 2

Answer 3

All th eterms are like words (all of them have one y in them) in an attempt to easily integrate: 1y + 3y - 2y = 2y (imagine that you've a million individual + 3 human beings - 2 human beings, that could want to provide you a effect of two human beings. Now merely replace the be conscious those with the letter "y")

Answer 4

1. 3x(squred) +21x
Pull out a three
X(squared) + 7x
Then it equals 3(x {squared} +7x
Thats the 1st one to help