To solve we must first write out what \(\displaystyle A-B\) is:

\(\displaystyle A-B=(3x^2+26x+108)-(12x-13)\)

Now,we can simplify. However, notice that when subtracting these terms, we subtract all terms in the parentheses. Remember when we subtract a negative number, it is the same as adding the number. This is illustrated in the simplification below.

\(\displaystyle (3x^2+26x+108)-(12x-13) = 3x^2+26x+108 - 12x- (-13)\)
 

This simplifies to \(\displaystyle 3x^2+26x+108 - 12x +13\)

Now we can combine like terms. Let's put those together and then simplify

\(\displaystyle 3x^2+26x+108 - 12x +13=3x^2+(26x - 12x)+(108 +13) = 3x^2+14x+121\)

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

When simplifying the addition or subtraction of polynomials, we want to combine like terms. First, when we have a negative sign outside our parentheses, we know that we need to distribute that negative; think of it as an imaginary \(\displaystyle -1\) and use the distributive property).

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

Then, we combine our like terms. Be careful when subtracting.

Rearrange the expression.

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

Combine terms and simplify.

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

\(\displaystyle \small x^2+4x^2-3x+2x-7-3x^2\)

Combine like terms.

\(\displaystyle \small (x^2+4x^2-3x^2)+(-3x+2x)-7\)

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

\(\displaystyle \small -3x+2x=-x\)

\(\displaystyle \small -7=-7\)

Add the terms together.

\(\displaystyle \small 2x^2+(-x)+(-7)=2x^2-x-7\)

In order to solve the problem, simply add the equations.

\(\displaystyle (10x^{2}+7x+5)+(3x^{2}-9x-8)\)

\(\displaystyle =10x^{2}+7x+5+3x^{2}-9x-8\)

Combine like terms.

\(\displaystyle =(10x^{2}+3x^{2})+(7x-9x)+(5-8)\)

Solve.

\(\displaystyle =13x^{2}-2x-3\)

When subtracting polynomials you only subtract the integers in front of like termed variables raised to the same power.

So in this case we take the numbers from in front of the variables and subtract them to get \(\displaystyle 3-5=-2\)

After subtraction we add the variable \(\displaystyle x^{5}\) to get \(\displaystyle -2x^{5}\).

The answer is \(\displaystyle -2x^{5}\).

According to exponent laws, if the bases are the same for the two numbers being divided, you keep the base and subtract the exponents.

Because both terms have the same radical,  \(\displaystyle \sqrt{5}\), you can combine terms.

\(\displaystyle (4+3) \sqrt{5})\) equals \(\displaystyle 7\sqrt{5}\)

When adding polynomials you only add the integers in front of like-termed variables raised to the same power.

So in this case we take the numbers and add \(\displaystyle 5+8=13\)

After addition we add the variable \(\displaystyle x^{16}\) to get \(\displaystyle 13x^{16}\). 

When subtracting polynomials you only subtract the integers in front of like-termed variables raised to the same power.

So in this case we take the numbers and subtract them \(\displaystyle 15-4=11\)

After subtraction we add the variable \(\displaystyle x^{13}\) to get \(\displaystyle 11x^{13}\).

The answer is \(\displaystyle 11x^{13}\).

When adding polynomials you only add the integers in front of like-termed variables raised to the same power.

So in this case we take the numbers with like-termed variables and combine them \(\displaystyle 4x^{5}-2x^{5}=2x^5\).

After subtraction we add the term \(\displaystyle 5x\) to get \(\displaystyle 2x^{5}+5x\).

The answer is \(\displaystyle 2x^{5}+5x\).