The distributive property involves multiplying each term inside of the parentheses by the term outside of the parentheses.  The distributive property is:

\(\displaystyle \dpi{100} a(b+c)=(a\times b)+(b\times c)\)

Remember: FOIL (first, outer, inner, last) to expand.

F: \(\displaystyle -2x^{2}\)

O: \(\displaystyle 5x\)

I: \(\displaystyle 6x\)

L: \(\displaystyle -15\)

Now you have four terms: \(\displaystyle -2x^{2}+5x+6x-15\)

Simplify: \(\displaystyle -2x^{2}+11x-15\)

When you multiply it out using the distributive property, you get \(\displaystyle 18+12\). Add those together to get \(\displaystyle 30\). 

\(\displaystyle (3*2)^2 - (2 - x) = 40\)

\(\displaystyle (6)^2 - 2 +x = 40\)

\(\displaystyle 36 - 2 + x = 40\)

\(\displaystyle 34 + x = 40\)

\(\displaystyle x = 6\)

By the distributive property, you must multiply both numbers within the parentheses by the number outside the parentheses. In this case, the expression becomes

 \(\displaystyle 18 -42x + 32 -16x = 50 - 58x\)

The distributive property involves multiplying the outside term by the first term in the parentheses and then adding/subtracting it to the product of the outside term and the second term of the parentheses. Since there's a plus sign, we're adding. Therefore, the result is \(\displaystyle \bigstar \bigoplus +\bigstar \blacktriangledown\).

The distributive property is needed to solve this problem. The distributive property is \(\displaystyle a(b+c)=(ab) + (cb)\). 

\(\displaystyle 3(x+8)=42\)
\(\displaystyle 3x + 24= 42\)

Now to solve for x we need to subtract 24 from both sides.      

\(\displaystyle 3x + 24= 42\)

        \(\displaystyle - 24 -24\)

From here we need to divide by 3.   
\(\displaystyle 3x=18\)
\(\displaystyle x=6\)

The distributive property is needed to solve this problem. The distributive property is \(\displaystyle a(b+c)= (ab) + (ac)\). In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.

\(\displaystyle (x+8)(x+7)\)
\(\displaystyle x\cdot x=x^2\)
\(\displaystyle x\cdot 7=7x\)
\(\displaystyle 8\cdot x=8x\)
\(\displaystyle 8\cdot 7=56\)

The final step to expand this expression is to combine like terms. Thus, the correct answer is 

\(\displaystyle x^2 + 15x + 56\)

The distributive property is needed to solve this problem. The distributive property is \(\displaystyle a(b+c)= (ab) + (ac)\). In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.   

\(\displaystyle (x-9)(x+3)\)
\(\displaystyle x\cdot x=x^2\)

\(\displaystyle x\cdot 3=3x\)

\(\displaystyle -9\cdot x=-9x\)

\(\displaystyle -9\cdot x=-9x\)

The last step to solving this problem is to combine like terms. Thus, the correct answer is:
\(\displaystyle x^2 - 6x - 27\)

The distributive property is needed to evaluate this expression. The distributive property is \(\displaystyle a(b+c)= (ab) + (ac)\)

\(\displaystyle 9(4-5)=?\)

We will apply the distributive property to both terms inside the parentheses.
\(\displaystyle 9\cdot 4=36\)
\(\displaystyle 9\cdot 5=45\)

Now we plug these values back into the expression to get:
\(\displaystyle 36-45=-9\)