Exponents and the Distributive Property - PSAT Math

Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.

Use FOIL:

(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.

(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)

(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.

The difference between A and B:

(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9

= - x2 - 4x - 9. Since all of the terms are negative and x > 0:

A - B < 0.

Rearrange A - B < 0:

A < B

First, move all terms to one side of the equation to set them equal to zero.

All terms contain an , so we can factor it out of the equation.

Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply to .

We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.

Our answer will be .

In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:

Next, multiply your first terms together:

Then, multiply your outside terms together:

Then, multiply your inside terms together:

Lastly, multiply your last terms together:

Together, you have

You can combine your like terms, , to give you the final answer:

Use the FOIL method (first, outside, inside, last) to find the product of:

First:

Outside:

Inside:

Last:

Sum the products to find the polynomial:

To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:

Then multiply the outside terms:

Next, multiply the inside terms:

Finally, multiply the last terms:

When you put the pieces together, you have . Notice that the middle terms cancel each other out, and you are left with . When you distribute the two, you reach the answer:

Take the square root of both sides.

Add 3 to both sides of each equation.

First calculate each section to yield 4c(27d3) – 8c3d + 2c4d4 = 108cd3 – 8c3d + 2c4d4. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d2 – 4c2 + c3d3).

= _x_3_y_3_z_3 + x_2_y + _x_0_y_0 + x_2_y

= _x_3_y_3_z_3 + x_2_y + 1 + x_2_y

= x_3_y_3_z_3 + 2_x_2_y + 1

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

Use the FOIL method to find the product. Remember to add the exponents when multiplying.

First:

Outside:

Inside:

Last:

Add all the terms:

Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.

Use FOIL:

(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.

(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)

(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.

The difference between A and B:

(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9

= - x2 - 4x - 9. Since all of the terms are negative and x > 0:

A - B < 0.

Rearrange A - B < 0:

A < B

First, move all terms to one side of the equation to set them equal to zero.

All terms contain an , so we can factor it out of the equation.

Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply to .

We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.

Our answer will be .

In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:

Next, multiply your first terms together:

Then, multiply your outside terms together:

Then, multiply your inside terms together:

Lastly, multiply your last terms together:

Together, you have

You can combine your like terms, , to give you the final answer:

Use the FOIL method (first, outside, inside, last) to find the product of:

First:

Outside:

Inside:

Last:

Sum the products to find the polynomial:

To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:

Then multiply the outside terms:

Next, multiply the inside terms:

Finally, multiply the last terms:

When you put the pieces together, you have . Notice that the middle terms cancel each other out, and you are left with . When you distribute the two, you reach the answer:

Take the square root of both sides.

Add 3 to both sides of each equation.

First calculate each section to yield 4c(27d3) – 8c3d + 2c4d4 = 108cd3 – 8c3d + 2c4d4. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d2 – 4c2 + c3d3).

= _x_3_y_3_z_3 + x_2_y + _x_0_y_0 + x_2_y

= _x_3_y_3_z_3 + x_2_y + 1 + x_2_y

= x_3_y_3_z_3 + 2_x_2_y + 1