The first step is to get everything out of parentheses to combine like terms. Since the polynomials are being subtracted, the sign of everything in the second polynomial will be flipped. You can think of this as a \(\displaystyle -1\) being distributed across the polynomial:

\(\displaystyle (14a^2 + 2a - 5) - (10a^2 - 3a + 8)\)

\(\displaystyle =(14a^2 + 2a - 5) + -1(10a^2 - 3a + 8)\)

\(\displaystyle =14a^2 + 2a - 5 - 10a^2 + 3a - 8\)

Now combine like terms:

\(\displaystyle 14a^2 + 2a - 5 - 10a^2 + 3a - 8\)

\(\displaystyle =4a^2 + 2a - 5 + 3a - 8\)

\(\displaystyle =4a^2 + 5a - 5 - 8\)

\(\displaystyle =4a^2 + 5a - 13\)

Don't be scared by complex terms! First, check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was \(\displaystyle 3x - 3x\).

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match! So we just subtract the coefficients of the matching terms and we get our answer:

\(\displaystyle 3 x^2 z^4+7 y^3 z^3\)

In simplifying this expression, be mindful of the order of operations (parenthical, division/multiplication, addition/subtraction).  

\(\displaystyle 5x^{^{3}} - 14x^{2} - 10x + 3 - (4x+3) * x^{2} - (8-10x)\)

Since operations invlovling parentheses occur first, distribute the factors into the parenthetical binomials. Note that the \(\displaystyle x^2\) outside the first parenthetical binomial is treated as \(\displaystyle -x^2\) since the parenthetical has a negative (minus) sign in front of it. Similarly, multiply the members of the expression in the second parenthetical by \(\displaystyle -1\) because of the negative (minus) sign in front of it. Distributing these factors results in the following polynomial.

\(\displaystyle 5x^3 - 14x^2 - 10x + 3 - 4x^3 - 3x^2 - 8 + 10x\)

Now like terms can be added and subtracted. Arranging the members of the polynomial into groups of like terms can help with this. Be sure to retain any negative signs when rearranging the terms.

\(\displaystyle 5x^3 - 4x^3 -14x^2 - 3x^2 - 10x + 10x + 3 - 8\)

Adding and subtracting these terms results in the simplified expression below.

\(\displaystyle x^3 - 17x^2 -5\)

First we convert each of the denominators into an LCD which gives us the following:

\(\displaystyle \frac{5\left ( x-2 \right )}{\left ( x+1 \right )\left ( x-2 \right )}- \frac{3x}{\left ( x+1 \right )\left ( x-2 \right )}= \frac{3\left ( x+1 \right )}{\left ( x+1 \right )\left ( x-2 \right )}\)

Now we add or subtract the numerators which gives us:

\(\displaystyle 5\left ( x-2 \right )-3x= 3\left ( x+1 \right )\)

Simplifying the above equation gives us the answer which is:

\(\displaystyle -13\)

\(\displaystyle 4x^3-2x(x-2)(x+3)\)

First, FOIL the two binomials:

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

Then distribute the \(\displaystyle 2x\) through the terms in parentheses:

\(\displaystyle 4x^3-2x^3-2x^2+12x\)

Combine like terms:

\(\displaystyle 2x^3-2x^2+12x\)

Simplify

\(\displaystyle (4a^{2}b+2ab) - (3a^{2}b+4ab+2)\)

Distribute the negative: \(\displaystyle \boldsymbol{-}3a^{2}b\boldsymbol{-}4ab\boldsymbol{-}2\)

Then combinde like terms

\(\displaystyle \mathbf{\boldsymbol{-}3a^{2}b+4a^{2}b}(\mathbf{\boldsymbol{-}4ab+2ab})\boldsymbol{-}2\)

Answer: 

\(\displaystyle a^{2}b-2ab-2\)

\(\displaystyle (7.5x^{2} + 1.4x - 4.6) - (x^{2} + 6.2x - 3.5)\)

\(\displaystyle = 7.5x^{2} + 1.4x - 4.6 - x^{2} - 6.2x + 3.5\)

\(\displaystyle = 7.5x^{2} - 1x^{2} + 1.4x- 6.2x - 4.6 + 3.5\)

\(\displaystyle = 6.5x^{2} - 4.8x - 1.1\)

\(\displaystyle \left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )\)

\(\displaystyle =\frac{1}{2}x + \frac{2}{3} - \frac{1}{4}x + \frac{1}{6}\)

\(\displaystyle =\frac{1}{2}x - \frac{1}{4}x + \frac{2}{3} + \frac{1}{6}\)

\(\displaystyle =\frac{2}{4}x - \frac{1}{4}x + \frac{4}{6} + \frac{1}{6}\)

\(\displaystyle =\frac{1}{4}x + \frac{5}{6}\)

\(\displaystyle (7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)\)

\(\displaystyle = 7.5x^{2} + 2.4x - 4.6 - x^{2} + 3.2x +1.5\)

\(\displaystyle = 7.5x^{2} - 1x^{2} + 2.4x + 3.2x - 4.6 +1.5\)

\(\displaystyle = 6.5x^{2} + 5.6x - 3.1\)

\(\displaystyle \left (\frac{3}{4}x + \frac{2}{5} \right ) - \left (\frac{1}{8}x - \frac{1}{10} \right )\)

\(\displaystyle =\frac{3}{4}x + \frac{2}{5} - \frac{1}{8}x + \frac{1}{10}\)

\(\displaystyle =\frac{3}{4}x- \frac{1}{8}x + \frac{2}{5} + \frac{1}{10}\)

\(\displaystyle =\frac{6}{8}x- \frac{1}{8}x + \frac{4}{10} + \frac{1}{10}\)

\(\displaystyle =\frac{5}{8}x + \frac{5}{10}\)

\(\displaystyle =\frac{5}{8}x + \frac{1}{2}\)