The associative property of multiplication states that you can multiply numbers together in any order, and the answer will not change.  Therefore, 

$\displaystyle (a \cdot b) \cdot c = a \cdot (b \cdot c)$

displays the associative property of multiplication since the two sides are equal no matter which set of parentheses you solve first.

Use the distributive property to multiply each term of the polynomial by $\displaystyle \small -2$. Be careful to distribute the negative as well.

$\displaystyle (-2)(x^2)+(-2)(x)-(-2)(8)$

$\displaystyle (-2x^2)+(-2x)-(-16)$

$\displaystyle -2x^2-2x+16$

We can seperate the problem into two steps:

$\displaystyle 2(3-2) = 2(1)=2$

$\displaystyle -4(2+5-7) = -4(0)=0$

We then combine the two parts:

$\displaystyle 2+0=2$

When distributing with negative numbers we must remember to distribute the negative to all of the variables in the parentheses.

Distribute the $\displaystyle -4$ through the parentheses by multiplying it with each object in the parentheses to get $\displaystyle ((-4)5x+(-4)15y-(-4)9)$.

Perform the multiplication remembering the positive/negative rules to get $\displaystyle -20x-60y+36$, our answer.

Multiply the mononomial by each term in the binomial, using the distributive property.

$\displaystyle (-x+2)(-xy)$

$\displaystyle (-xy)(-x)+(-xy)(2)$

$\displaystyle x^2y+(-2xy)$

$\displaystyle x^2y-2xy$

$\displaystyle 2x(5+4x+y)$

Use the distributive property to multiply each term by $\displaystyle \small 2x$.

$\displaystyle 2x(5)+2x(4x)+2x(y)$

Simplify.

$\displaystyle 10x+8x^2+2xy$

When distributing with negative numbers we must remember to distribute the negative to all of the terms in the parentheses.

Remember, a negative multiplied by a negative is positive, and a negative multiplied by a positive number is negative.

Distribute the $\displaystyle -3$ through the parentheses:

$\displaystyle -4x(-3)+5y(-3)-8(-3)$

Perform the multiplication, remembering the positive/negative rules:

$\displaystyle 12x-15y+24$

We need to distribute -3 by multiplying both terms inside the parentheses by -3.:

 $\displaystyle -3(2d - 4) = -3(2d) + (-3)(-4)$.

Now we can multiply and simplify. Remember that multiplying two negative numbers results in a positive number:

$\displaystyle -3(2d)+(-3)(-4)= -6d + 12$

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

Use the distributive property. Do not forget that the negative sign needs to be distributed as well!

$\displaystyle \small \small (-4x)(3x^2)=-12x^3$

$\displaystyle \small (-4x)(-7x)=28x^2$

$\displaystyle \small (-4x)(2)=-8x$

Add the terms together:

$\displaystyle \small -12x^3+28x^2+(-8x)=-12x^3+28x^2-8x$

Remember that a negative multiplied by a negative is positive, and a negative multiplied by a positive is negative.

Distribute the $\displaystyle -5$ through the parentheses by multiplying it by each of the two terms: 

$\displaystyle -5x-75$