We are subtracting here, so it is important to remember that subtracting is really just adding the same number with opposite sign. Thus we can think of the problem as the following: 

\(\displaystyle (-5) + (-2)\), which we know is equal to \(\displaystyle -7\).

Recall that subtracting integers is equivalent to adding the inverse. The inverse of a negative number is the positive number with the same magnitude.

Thus, our problem is equivalent to \(\displaystyle 10 + 2 = 12\).

Recall that subtracting is equivalent to adding the inverse:

\(\displaystyle -2 - (-4) = -2 + (-(-4))\)

The inverse of a negative number is a positive number:

\(\displaystyle -2 - (-4) = -2 + 4 = 2\)

Recall the placement of numbers on the number line. \(\displaystyle -4\) is \(\displaystyle 4\) spaces to the left of \(\displaystyle 0\), and then we add \(\displaystyle 8\), resulting in movement to the right. 

When we add these spaces we end up going \(\displaystyle 4\) spaces back to \(\displaystyle 0\) and then \(\displaystyle 4\) additional spaces to end at \(\displaystyle 4\). 

Recall that subtracting a negative number is equivalent to adding the opposite. Thus, \(\displaystyle 8 - (-3) = 8 + 3 = 11\)

Recall that subtracting negative numbers is equivalent to adding the opposite. Then, we have that: 

\(\displaystyle -3 - (-5) = -3 + 5 = 2\)

In this case, it is key to recall the rules for multiplying or dividing with negative values.

Negative * Positive = Negative

Negative * Negative = Positive

Positive * Positive = Positive

In this case, we are multiplying two negative numbers; thus the answer should be a positive number. To find the value, we can simply multiply the terms without their negatives.

\(\displaystyle -5*-3=5*3=15\)

First multiply all the numbers \(\displaystyle (2 \cdot 3 \cdot 5)\).

If there is an even amount of negative signs, then the product will be positive. If there is an odd amount of negative signs, then the product will be negative.

\(\displaystyle y\cdot y=y^{2}\)

Therefore, the answer is \(\displaystyle 30y^2\).  

First multiply according to order of operations to get 6xy, and then see if there are like terms to be combined. In this case, there are not so the simplest form is \(\displaystyle 2x*3y-2y+3x=0\)

A number is prime if it is divisible by only itself and one. Thus, if a number is divisible by anything else, it can't be prime. Of the answer choices, only 427 isn't prime, because it is divisible by 7.

To figure out which number is prime, one strategy you could employ is using your calculator and dividing each choice by 3, 7, 9, 11, and 13. Because all of the answer choices are odd, we know none of them will be divisible by 2, 4, 6, 8, or 10. Also, none of them have a 0 or 5 in the ones place, so they can't be divisible by 5. Thus, the best numbers to try would be 3, 7, 9, 11, and 13. When you divide 427 by 7, you will get a whole number. For all the other answer choices, when you divide by 3, 7, 9, 11, and 13, you will never get a whole number.

The answer is 427.