First, distribute –5 through the parentheses by multiplying both terms by –5.

\(\displaystyle -5(x+15)-3x=-5x-75-3x\)

Then, combine the like-termed variables (–5x and –3x).

\(\displaystyle -5x-75-3x=-8x-75\)

First, FOIL:

\(\displaystyle \frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+\frac{12}{3})\)

Simplify:

\(\displaystyle \frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+4)\)

Distribute the \(\displaystyle \frac{1}{3}\) through the parentheses:

\(\displaystyle \frac{8}{3}x^3-\frac{4}{9}x^2-\frac{24}{3}x+\frac{4}{3}\)

Rewrite to make the expression look like one of the answer choices:

\(\displaystyle 2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}\)

\(\displaystyle \textup{Factor the quadratic into two binomials.}\)\(\displaystyle \, \:\left( x+a\right )\left ( x+b\right )\)

\(\displaystyle \textup{The sum of the missing numbers is the coefficient of }4x\).

\(\displaystyle \textup{The product of these numbers is the constant in the quadratic.}\)

\(\displaystyle a+b=4\:\:\:a\times b=3\:\:\textup{Therefore, }a\textup{ and }b\textup{ are 1 and 3.}\)

\(\displaystyle \left ( x+3\right )\left ( x+1\right )=0\:\:\:x= -3\textup{ or }-1\)

Use the FOIL method, which stands for First, Inner, Outer, Last:

\(\displaystyle (4x)(-2x)+(4x)(3)+(-1)(-2x)+(-1)(3)\)

\(\displaystyle = -8x^2+12x+2x-3\)

\(\displaystyle =-8x^{2}+14x-3\)

The distributive property is handy to help get rid of parentheses in expressions. The distributive property says you "distribute" the multiple to every term inside the parentheses. In symbols, the rule states that 

\(\displaystyle a(b+c)=ab+ac\)

So, using this rule, we get \(\displaystyle 4(3x^2+5x-2) =4*3x^2+4*5x-4*2) = 12x^2+20x-8\)

Thus we have our answer is \(\displaystyle 12x^2+20x-8\).

To multiple these binomials, you can use the FOIL method to multiply each of the expressions individually.This will give you

\(\displaystyle (x)(3x)+(x)(2)+(-9)(3x)+(-9)(2)\)

or \(\displaystyle 3x^{2}-25x-18\).

In order to multiply the binomials, we will need to multiply each term of the first binomial with the terms of the second binomial.

\(\displaystyle (x+9)(8-x) = (x)(8)+(x)(-x)+(9)(8)+(9)(-x)\)

Simplify each term.

\(\displaystyle 8x-x^2+72-9x\)

Combine like terms and reorder the powers from highest to lowest order.

The answer is:  \(\displaystyle -x^2-x+72\)

Multiply each term of the first binomial with the terms of the second binomial.

\(\displaystyle (3)(y)+(3)(-z)+(-x)(y)+(-x)(-z)\)

Simplify the terms of this expression.

\(\displaystyle 3y-3z-xy+xz\)

There are no like terms to simplify.

The answer is:  \(\displaystyle 3y-3z-xy+xz\)

Multiply each term of the first binomial with the second binomial and add the terms. 

\(\displaystyle 9(3+6x) +(-2x)(3+6x)\)

Simplify by distribution.

\(\displaystyle 27+54x-6x-12x^2\)

Combine like-terms.

\(\displaystyle 27+48x-12x^2\)

The answer is:  \(\displaystyle -12x^2+48x+27\)

\(\displaystyle (-x+10)(3x^{2}-4)\)

Use the FOIL method to multiply the binomials given.

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

O: \(\displaystyle -x(-4)=4x\)

I: \(\displaystyle 10(3x^{2})=30x^{2}\)

L: \(\displaystyle 10(-4)=-40\)

Group any like terms (none for this problem) when putting all the terms back together.

\(\displaystyle -3x^{3}+30x^{2}+4x-40\)