To simplify, first remember to distribute the negative sign in front of the second set of terms:

$\displaystyle 6x-3y+10+2x-10y+12$.

Then, combine like terms.

Your answer is:

$\displaystyle 8x-13y+22$.

To simplify this expression, first identify the greatest common factor for this set of terms.

In this case, it's 4.

Then, factor 4 out of each of the terms to get your answer of:

$\displaystyle 4(4x^2-16x+7)$.

In order to multiply both terms, first distribute the first term of the first polynomial with the the second polynomial.

$\displaystyle 2x^2(x^2-4x-5) = 2x^4-8x^3-10x^2$

Repeat the process for the second and third terms.

$\displaystyle 3x(x^2-4x-5)=3x^3-12x^2-15x$

$\displaystyle 2(x^2-4x-5) = 2x^2-8x-10$

Add all the trinomials together and combine like-terms.

$\displaystyle (2x^4-8x^3-10x^2)+(3x^3-12x^2-15x)+(2x^2-8x-10)$

The answer is:  $\displaystyle 2x^4-5x^3-20x^2-23x-10$

To simplify this expression, combine all like terms:

$\displaystyle 4x^2+9x^2=13x^2$

$\displaystyle -x-11x=-12x$

Put your simplified terms together:

$\displaystyle 5x^3+13x^2-12x$

The first step here is to use the distributive property:

$\displaystyle 9x^2-36+10x+15$

Now combine your like terms to get your final answer:

$\displaystyle 9x^2+10x-21$

Simplify the polynomial.

$\displaystyle 4x^2+7x-3-2x^2+6x+9$

Step 1: Rearrange the expression so that like terms are next to each other.

Remember: Like terms are terms with the same type of variable.

$\displaystyle 4x^2-2x^2+7x+6x-3+9$

Step 2: Simplify by adding or subtracting like terms.

$\displaystyle 2x^2+13x+6$

Solution: $\displaystyle 2x^2+13x+6$

In order to correctly simplify this problem you must pay attention to which terms are actually considered "like terms" and pay attention to signs. For instance 6x and 6x^2 are not like terms. Neither are 3 and 3x.

$\displaystyle 5x^4+x^4+3x^2-8+3x-x(3+8x)-10$

Start by distributing within the parenthesis:

$\displaystyle 5x^4+x^4+3x^2-8+3x-3x-8x^2-10$

Next simplify the like terms based on your preference. We will start with the highest powers (largest exponents):

$\displaystyle 6x^4+3x^2-8+3x-3x-8x^2-10$

Now the squared exponents:

$\displaystyle 5x^4+x^4-5x^2-8+3x-3x-10$

Now the x terms cancel and simplify the constants:

$\displaystyle 6x^4-5x^2-18$

This is a difference of perfect cubes so it factors to $\displaystyle (x-1)(x^2+x+1)$. Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the $\displaystyle x$-axis. Therefore, your answer is only 1.

Factor the equation to $\displaystyle 2x(x^4-4x^2+4)$. Set $\displaystyle 2x=0$ and get one of your $\displaystyle x$'s to be $\displaystyle 0$. Then factor the second expression to $\displaystyle (x^2-2) (x^2-2)$. Set them equal to zero and you get $\displaystyle \pm \sqrt{2}$. 

First, begin by factoring out a common term, in this case $\displaystyle 16x$:

$\displaystyle 16x^{3} -48x^{2} + 32x = 16x(x^{2}-3x+2)$

Then, factor the terms in parentheses by finding two integers that sum to $\displaystyle -3$ and multiply to $\displaystyle 2$:

$\displaystyle 16x(x-2)(x-1)$