I do not understand how to subtract binomials, trinomials, and monomials.?

Question

9: (19x5 - 14x3 + 9x) + (19x7 - 8x3 - 12)

19x7 - 22x3 + 9x - 12

19x6 + 19x5 - 22x3 - x - 12

19x7 + 19x5 - 22x3 + 9x - 12

10: (18x2 - 4x - 12) + (-8x2 + 16x - 18)

10x2 + 12x + 30

10x2 + 12x - 30

x2 + 12x - 30

An explanation of how to do these two problems would be greatly appreciated. Thanks in advance !

Answer 1

Only factors with the same exponents can be added and subtracted.

in question 9   19x^5 and 19x^7 and 9x^1 (9x = 9x^1) and -12x^0 (-12 = -12x^0)won't be added or subtracted because they stand alone

but -14x3 and -8x3 have the same power so you add them together to get -22x^3

thus you write your answer with the factor with the highest exponent (x^7)

and will look like this:  19x^7 + 19x^5 - 22x^3 + 9x - 12

Answer 2

First of all, you should use proper notation. x squared = x^2

Secondly, when subtracting polynomials from other polynomials, you must distribute the subtraction operation to all of the terms in the polynomial fallowing the minus symbol. Once you distribute the subtraction symbol through the entire second polynomial, you can simply add them.

Answer 3

You have to add "like terms".  These pages give a good written explanation:

http://mathforum.org/library/drmath/view...

http://mathforum.org/library/drmath/view...