Distributive Property - SAT Math

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

Remember that (a – b )(a + b ) = a 2 – b 2.

We can therefore rewrite (3_x –_ 4)(3_x_ + 4) = 2 as (3_x_ )2 – (4)2 = 2.

Simplify to find 9_x_2 – 16 = 2.

Adding 16 to each side gives us 9_x_2 = 18.

We are asked to find the difference between g(h(x)) and h(g(x)), where g(x) = 2x2 – 2 and h(x) = x + 4. Let's find expressions for both.

g(h(x)) = g(x + 4) = 2(x + 4)2 – 2

g(h(x)) = 2(x + 4)(x + 4) – 2

In order to find (x+4)(x+4) we can use the FOIL method.

(x + 4)(x + 4) = x2 + 4x + 4x + 16

g(h(x)) = 2(x2 + 4x + 4x + 16) – 2

g(h(x)) = 2(x2 + 8x + 16) – 2

Distribute and simplify.

g(h(x)) = 2x2 + 16x + 32 – 2

g(h(x)) = 2x2 + 16x + 30

Now, we need to find h(g(x)).

h(g(x)) = h(2x2 – 2) = 2x2 – 2 + 4

h(g(x)) = 2x2 + 2

Finally, we can find g(h(x)) – h(g(x)).

g(h(x)) – h(g(x)) = 2x2 + 16x + 30 – (2x2 + 2)

= 2x2 + 16x + 30 – 2x2 – 2

= 16x + 28

The answer is 16x + 28.

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.

Let the two numbers be x and y.

x + y = s

xy = p

(x + 1)(y + 1) = q

Expand the last equation:

xy + x + y + 1 = q

Note that both of the first two equations can be substituted into this new equation:

p + s + 1 = q

Solve this equation for q – p by subtracting p from both sides:

s + 1 = q – p

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

Which becomes

Or, written better

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 .

Use the FOIL method in the distributive property to simplify the expression:

First simplify the radicals,

Use the FOIL method to distribute terms and simplify the equation:

Use the FOIL method (first, outer, inner, last) to multiply expressions and combine like terms:

Use the FOIL method to simplify. Use the following formula to simplify.

Substitute and follow the terms.

Combine like terms.

The answer is :

Use the FOIL method to solve. Follow the example below:

Simplify the expression.

The answer is:

Using the FOIL method for multiplying binomial expressions:

If a problem asks you to expand an expression, you must use the Distributive property. If you are using the FOIL method, you first multiply the first term in each parentheses by each other, followed by the outside terms, then the inside terms, and then the last terms. This is illustrated below.

First, you multiply which equals

Second, you multiply

Third, you multiply

Last, you multiply

Then you simply rearrange them in order of exponents to get

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this: