matth again! helllp?

Question

Polynomials!

(10m-4)-(3m-5)=
(k²-2k+5)-(k²+5k+3)=
(2x²+7x-4)-(x²-4)=
2x²+4+(3x²-4x-5)=
(-2x²+4x-5)+(8x+5x²+6)=
(3x²y²+2xy+5y)-(-2x²y²-4x+5y)=
(7x^3-5x²-3x+8)-(10x^3-4x²+5x+9)=

2x^3-5x²-5+3x^3+7x²+9x=
-4x²y²+3xy+x2-4y2+x²y²-6xy-x²-5y2=
(x²+2y+5)-(4x+4y)=
(-4a²b+7ab²-9a-6b+13)-(-6a²b+8a+10b-18)=

Answer 1

For addition of polynomials, you add term with like powers by adding the coefficients of the unknown coefficient. In the first example, you have "x" to the second power terms, so you add the coefficients "2" and "3" to get 5x^2. If you have just constants, add them together. In this example, 4 and -5 are -1. SIGNS ARE IMPORTANT.

With subtraction, you first must convert the process to an addition by changing ALL THE SIGNS of the term to be subtracted. Thus, in the first example, the addition is of 10m-4-3m+5, or 7m+1.

With the last bunch, you are COLLECTING LIKE TERMS and adding their coefficients. In the first example, the "x-cubed" terms are 2x^3 and 3x^3, so their collection yields 6x^3. With multi-variables, the like term must be EXACTLY ALIKE. So in example 2, the "x^2y^2" terms are added together which are -4x^2y^2 and x^2y^2 to get -3x^2y^2.

With this explanation, you should be able to rip through your problems lickety-split.

Answer 2

distribute the negative signs through the polynomial. then the rest is just adding and subtracting.