Subtract the first expression from the second to get the following:

\(\displaystyle x^{5}-4x^{4}-2x^{3}-9xy - \left ( -3x^{3}+2x^{2}-xy -13 \right )\)

This is equal to:

\(\displaystyle x^{5}-4x^{4}-2x^{3}-9xy+3x^{3}-2x^{2}+xy+13\)

Combine like terrms:

\(\displaystyle x^{5}-4x^{4}+x^{3}-2x^{2}-8xy+13\)

\(\displaystyle (x^2+3.5x+10)-(5x^2-1.5x+2)=x^2+3.5x+10-5x^2+1.5x-2\)

\(\displaystyle =x^2-5x^2+3.5x+1.5x+10-2=-4x^2+5x+8\)

You must multiply out the first set of parenthesis (distribute) and you get 4x – x². Then multiply out the second set and you get –3x + x². Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x² – x(3 – x)

4x – x² – (3x – x²)

4x – x² – 3x + x² = x

\(\displaystyle (3p^{2}+8)+(-p^{2}+5)\)

This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.

Add like terms to solve.

\(\displaystyle 3p^{2}-p^{2}=2p^{2}\)

\(\displaystyle 8+5=13\)

Combining these terms into an expression gives us our answer.

\(\displaystyle 2p^{2}+13\)

When simplifying polynomials, only combine the variables with like terms.

\(\displaystyle 15x^{3}y^{2}\) can be added to \(\displaystyle 3x^{3}y^{2}\), giving \(\displaystyle 18x^{3}y^{2}\). 

\(\displaystyle 4x^{2}\) can be subtracted from \(\displaystyle 8x^{2}\) to give \(\displaystyle 4x^{2}\).

Combine both of the terms into one expression to find the answer: \(\displaystyle 18x^{3}y^{2}+4x^{2}\)

\(\displaystyle (5c^{2}+5)+(-5c-5)\)

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms to solve.

\(\displaystyle 5c^{2}\) and \(\displaystyle -5c\) have no like terms and cannot be combined with anything.

5 and -5 can be combined however:

\(\displaystyle 5-5=0\)

This leaves us with \(\displaystyle 5c^{2}-5c\).

LCM of \(\displaystyle 2,4,6=12\)

LCM of \(\displaystyle x, x^{2}=x^{2}\)

and since \(\displaystyle \left ( x^{2} -1 \right )= \left ( x+1 \right )\left ( x-1 \right )\)

The LCM  \(\displaystyle =12x^{2}\left ( x+1 \right )(x-1)\)

First factor the denominators which gives us the following:

\(\displaystyle \frac{x}{\left ( x+1 \right )\left ( x-3 \right )} + \frac{1}{\left ( x+1 \right )\left ( x-3 \right )}\)

The two rational fractions have a common denominator hence they are like "like fractions".  Hence we get:

\(\displaystyle \frac{x+1}{\left ( x+1 \right )\left ( x-3 \right )}\)

Simplifying gives us

\(\displaystyle \frac{1}{x-3}\)

\(\displaystyle (2x^{2}-5) + (4x^{3}-3x^{2}+2x-1)\)

To simplify you combind like terms: 

\(\displaystyle (4x^{3}\boldsymbol{-3x^{2}+2x^{2}} +2x\boldsymbol{-1-5)}\)

Answer: 

\(\displaystyle 4x^{3}-x^{2}+2x-6\)

When combining polynomials, only combine like terms. With the like terms, combine the coefficients. Your answer is \(\displaystyle -9x^2y^3z+6m^4n^5\).