When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.

Which becomes

Or, written better

Multiply using FOIL:

First = 3x(2x) = 6x²

Outter = 3x(4) = 12x

Inner = -1(2x) = -2x

Last = -1(4) = -4

Combine and simplify:

6x² + 12x - 2x - 4 = 6x² +10x - 4

Solve by applying FOIL:

First: 2x² * 2y = 4x²y

Outer: 2x² * a = 2ax²

Inner: –3x * 2y = –6xy

Last: –3x * a = –3ax

Add them together: 4x²y + 2ax² – 6xy – 3ax

There are no common terms, so we are done.

Use FOIL to expand the left side of the equation.

From this equation, we can solve for , , and .

Plug these values into to solve.

We can solve by FOIL, then distribute the . Since all terms are being multiplied, you will get the same answer if you distribute the before using FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify. Do not forget the in front of the quadratic!

Finally, distribute the .

To find what  equals, you must know how to multiply  times , or, you must know how to multiply binomials. The best way to multiply monomials is the FOIL (first, outside, inside, last) method, as shown below:

Multiply the First terms

Multiply the Outside terms:

Multiply the Inside terms:

Note: this step yields a negative number because the product of the two terms is negative.

Multiply the Last terms:

Note: this step yields a negative number too!

Putting the results together, you get:

Finally, combine like terms, and you get:

First pull out any common terms: 4x³ – 16x = 4x(x² – 4)

x² – 4 is a difference of squares, so we can also factor that further. The difference of squares formula is a² – b² = (a – b)(a + b). Here a = x and b = 2. So x² – 4 = (x – 2)(x + 2).

Putting everything together, 4x³ – 16x = 4x(x + 2)(x – 2).

The correct answer is (x + 4)(x – 4) 

We neen to factor x² – 16 to solve. We know that each parenthesis will contain an x to make the x². We know that the root of 16 is 4 and since it is negative and no value of x is present we can tell that one 4 must be positive and the other negative. If we work it from the multiple choice answers we will see that when multiplying it out we get x² + 4x – 4x – 16. 4x – 4x cancels out and we are left with our answer. 

First, let's factor x³ – y³ using the formula for difference of cubes.

x³ – y³ = (x – y)(x² + xy + y²)

We are told that x² + xy + y² = 6. Thus, we can substitute 6 into the above equation and solve for x – y.

(x - y)(6) = 30.

Divide both sides by 6.

x – y = 5.

The original questions asks us to find x² – 2xy + y². Notice that if we factor x² – 2xy + y² using the formula for perfect squares, we obtain the following:

x² – 2xy + y² = (x – y)².

Since we know that (x – y) = 5, (x – y)² must equal 5², or 25.

Thus, x² – 2xy + y² = 25.

The answer is 25.