Use substitution to determine the relationship.

For example, we could plug in  and .

So far it looks like the first expression is greater, but it's a good idea to try other values of x and y to be sure. This time, we'll try some negative values, say,  and .

This time the first quantity is smaller. Therefore the relationship cannot be determined from the information given.

We have three variables and only two equations, so we will not be able to solve for each independent variable. We need to think of another solution.

Notice what happens if we line up the two equations and add them together. 

(x + y) + (3x – y + z) = 4x + z

and 5 + 3 = 8

Lets take this equation and multiply the whole thing by 3:

3(4x + z = 8)

Thus, 12x + 3z = 24.

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x² and -4 by 3.

x³ - 4x² -12 + 15

You can then add -12 and 15, which equals 3.

You now have x³ - 4x² + 3 and are finished. Just a reminder that x³ and 4x² are not like terms as the x’s have different exponents.

First, we can use the property of exponents that x^y/x^z = x^y–z

Then we can use the property of exponents that states x^–y = 1/x^y

a^–1b⁵c^–1 = b⁵/ac

Begin by distributing each part:

2x(x² + 4ax – 3a²) = 2x * x² + 2x * 4ax – 2x * 3a² = 2x³ + 8ax² – 6a²x

The second:

–4a²(4x + 3a) = –16a²x – 12a³

Now, combine these:

2x³ + 8ax² – 6a²x – 16a²x – 12a³

The only common terms are those with a²x; therefore, this reduces to

2x³ + 8ax² – 22a²x – 12a³

This is the same as the given answer:

–12a³ – 22a²x + 8ax² + 2x³

To simplify this, we will want to use the correct order of operations. The mnemonic device PEMDAS is usually very helpful.

Parenthesis (1st)

Exponents (2nd)

Multiply, Divide (3rd)

Add, Subtract (4th)

PEMDAS tells us to evaluate parentheses first, then exponents. After exponents, we evaluate multiplication and division from left to right, and then we evaluate addition and subtraction from left to right.

Let's look at (xy)² – x((4x)(y)² – (4x)²) – 4²x²

We want to start with parentheses first. We will simplify the (xy)² by using the general rule of exponents, which states that (ab)^c = a^cb^c. Thus we can replace (xy)² with x²y².

x²y² – x((4x)(y)² – (4x)²) – 4²x²

When we have parentheses within parentheses, we want to move from the innermost parentheses to the outermost. This means we will want to simplify the expression (4x)(y)² – (4x)² first, which becomes 4xy² – 16x². We can now replace (4x)(y)² – (4x)² with 4xy² – 16x² .

x²y² – x(4xy² – 16x²) – 4²x²

In order to remove the last set of parentheses, we will need to distribute the x to  4xy² – 16x² . We will also make use of the property of exponents which states that a^ba^c = a^b+c.

x²y² – x(4xy²) – x(16x² ) – 4²x²
= x²y² – 4x²y² – 16x³ – 4²x²

We now have the parentheses out of the way. We must now move on to the exponents. Really, the only exponent we need to simplify is –4², which is equal to –16. Remember that –4² = –(4²), which is not the same as (–4)².

x²y² – 4x²y² – 16x³ – 16x²

Now, we want to use addition and subtraction. We need to add or subtract any like terms. The only like terms we have are x²y² and –4x²y². When we combine those, we get –3x²y²

–3x²y² – 16x³ – 16x²

The answer is –3x²y² – 16x³ – 16x² .

 can also be expressed as 

5x – (6x – 2x) = 5x – (4x) = x

(x – 1)(x + 2) - x² + 2 = x² + x – 2 – x² + 2 = x

x(4x)/(4x) = x

(3 – 3)x = 0x = 0

Step 1: 7x + 3y

Step 2: 4 * (7x + 3y) = 28x + 12y

Step 3: 28x + 12y + x = 29x + 12y

Step 4: 29x + 12y – (x – y) = 29x + 12y – x + y = 28x + 13y

Use PEMDAS to dictate which operation comes first. Simplify the parentheses:
  and

.

Next come exponents:

After that comes multiplication and division left to right:

 and

.

Finally, add all the terms together: