10y+7x2+3y

Question

I need help with some math problems. I need some directions or steps that will show me how to solve problems such as combining like terms. 

 

Answer 1

 Terms are constituent of Algebraic expressions, separated from each other by ( + , -)

 

 Terms consisted of factors that are separated from each other by multiplication or division.

 

    Consider :  Expression 

 

      2 XY + 3 zX + X ^2 - 3 X^2 + 5XY   ( 1)

 

     All underlined entities are terms which make the expression

 

      2 XY  -- is a term consist of factors 2, X and Y

 

     The constants factors are called coefficients.

 

      Like terms are the terms which have same variable factors with the same exponents.

 

      2XY , and 5XY are like terms

 

      X² , -3X^2 are like terms as well.

 

     To Simplify an algebraic expression, only like terms add up, and expression simplifies to the single like term with coefficient as algebraic sum of the coefficient of each.

     Expression ( 1) simplifies to:

 

   7XY + 3 ZX - 2 X^2 

 

   10 Y + 7 X^2 + 3Y = 10 Y + 7 X^2

      

Answer 2

So the first step to this is to identify like terms.  To do this, you need to know what a term is.  A term is made up of two parts, the coefficient (the number in front of the term) and the variable term (the part that has letters, like x in it).

 

So for two terms to be like terms, the variable part has to be equivalent.  A few examples is 3x, 12x.  Both variable terms are x, so they are a like.  Another example is 4xy, -8yx.  Since xy is the same thing as yx, they are like terms.  And out of 4x, 5y, -2y², 9x, 33y²;  -2y² and 22y² are like terms since they have the same variable term y² and also 4x and 9x are like terms since they both have the same variable term x.

 

Now once you have identified the like terms, you want to combine them.  You do that by adding the coefficients (the numbers in front of the term).  Remember, if there is no number, the coefficient is 1.

 

So now, with your problem, I am not sure if that x is supposed to by multiplication, or a variable.  I will do it with both.

 

So, if the x is a variable, then we can rewrite the term 7x2 as 14x since 7x2 is all multiplication, and we can just multiply the numbers together, even though they are not next to each other.  Just like with 3*4*5, we can first multiply 3 and 5 together, to get 15, then times 4 to get 60 is the same thing as doing it in order.

Thus the equation simplifies down to 10y +14x +3y.  Now we identify our like terms.  They are 10y and 3y.  To combine them, we add the coefficients, 10 and 3, to get 13.  So after combining the like terms the equation will look like 13y +14x.

 

Now if that x means to multiply, then 10y + 7x2 +3y = 10y +14 + 3y.  Again, our like terms are 10y and 3y.  So combining them, we will get 13y making the final result to be 13y+14.

 

I hope you were able to follow this.  It might be a bit more information than you needed, but I like being thorough.  Hope it helps.