SOLUTION: I am not very good at math and need a lot of help and detail! I think to hard on every question and I feel that i can not get anything right. I am in advanced math in 8th grade and

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Question 604393: I am not very good at math and need a lot of help and detail! I think to hard on every question and I feel that i can not get anything right. I am in advanced math in 8th grade and I am just trying to get through this last quarter without failing so that i can to alegbra 1 again next year. I really need help on binomials which i have problem i cant get which is...( and i cant the square numbers which are the little numbers next to the x's so all the x's have a square little number which are the x4, x3,and x2)

x4 (y+1)+2(y+1)x3 +x2 (y+1)

can u get that problem for me. Also can you tell me the difference in binomilas and trinomials?
Thanks sooo much this means a lot
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E3 is a monomial, a group of one or more numbers and/or symbols multiplied together, with no plus or minus signs. Monomials can be as simple as x or 2, or not so simple as 24x%5E5y%5E2z%5E3.

y%2B1 and 4x%5E2-9y%5E4 are both binomials because each has 2 groups of symbols and/or numbers (2 monomials) separated by plus and/or minus signs. The "bi" part means 2, as in bicycle.

x%5E2-5x%2B6 is a trinomial because there are 3 groups of symbols and numbers separated by plus and/or minus signs. The "tri" part means 3, as in tricycle.
The binomials x-3 and x-2 can be multiplied together and the result is the trinomial x%5E2-5x%2B6 :
%28x-2%29%28x-3%29=x%5E2-3x-2x%2B6=x%5E2-5x%2B6

To start, the expression
x%5E4%28y%2B1%29%2B2%28y%2B1%29x%5E3%2Bx%5E2%28y%2B1%29 can be simplified by
"taking out" the common factor %28y%2B1%29 .


The trinomial x%5E4%2B2x%5E3%2Bx%5E2 in that expression can be factored further.
To begin, we can "take out" the common factor x%5E2
x%5E4%2B2x%5E3%2Bx%5E2=x%5E2%28x%5E2%2B2x%2B1%29

Then, the trinomial x%5E2%2B2x%2B1 can be factored further. It happens to be the square of the binomial x%2B1
%28x%2B1%29%5E2=x%5E2%2B2x%2B1

So in 3 steps, we can factor x%5E4%28y%2B1%29%2B2%28y%2B1%29x%5E3%2Bx%5E2%28y%2B1%29 completely: