Exponents and the Distributive Property - PSAT Math
Card 0 of 11
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Compare your answer with the correct one above
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
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
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
Compare your answer with the correct one above
Solve for all real values of 
.
Solve for all real values of
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 
.
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an
Now, we can factor the quadratic in parenthesis. We need two numbers that add 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
Compare your answer with the correct one above
Simplify: 
Simplify:
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: 
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,
Compare your answer with the correct one above
Use FOIL to simplify the following product:
Use FOIL to simplify the following product:
Use the FOIL method (first, outside, inside, last) to find the product of:
First: 
Outside: 
Inside: 
Last: 
Sum the products to find the polynomial:
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Compare your answer with the correct one above
Simplify:
Simplify:
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: 
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
Compare your answer with the correct one above
If 
, which of the following could be the value of 
?
If
Take the square root of both sides.
Add 3 to both sides of each equation.
Take the square root of both sides.
Add 3 to both sides of each equation.
Compare your answer with the correct one above
Which of the following is equivalent to 4c(3d)3 – 8c3d + 2(cd)4?
Which of the following is equivalent to 4c(3d)3 – 8c3d + 2(cd)4?
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).
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).
Compare your answer with the correct one above
Simplify:
Simplify:
= _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
= _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
Compare your answer with the correct one above
Square the binomial.
Square the binomial.
We will need to FOIL.
First: 
Inside: 
Outside: 
Last: 
Sum all of the terms and simplify.
We will need to FOIL.
First:
Inside:
Outside:
Last:
Sum all of the terms and simplify.
Compare your answer with the correct one above
Use the FOIL method to find the product. Remember to add the exponents when multiplying.
First: 
Outside: 
Inside: 
Last: 
Add all the terms:
Use the FOIL method to find the product. Remember to add the exponents when multiplying.
First:
Outside:
Inside:
Last:
Add all the terms:
Compare your answer with the correct one above