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.

\(\displaystyle 10x+8x^2+2xy\)

Recall that the distributive property requires that we multiply the outside term by both terms in parentheses and add the results. 

\(\displaystyle 5(x+2) = 5\cdot x + 5\cdot2 = 5x + 10\)

Recall the distributive property. We need to multiply the outside factor by both terms inside and then combine. 

Thus, 

\(\displaystyle -2(3x + 4) = -2(3x) + (-2)(4) = -6x + (-8) = -6x - 8\)

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:

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