All SAT Math Resources
Example Question #1 : Distributive Property
Example Question #2 : Distributive Property
If , what is the value of ?
Remember that (a – b )(a + b ) = a 2 – b 2.
We can therefore rewrite (3x – 4)(3x + 4) = 2 as (3x )2 – (4)2 = 2.
Simplify to find 9x2 – 16 = 2.
Adding 16 to each side gives us 9x2 = 18.
Example Question #3 : Distributive Property
If and , then which of the following is equivalent to ?
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.
Example Question #4 : Distributive Property
The sum of two numbers is . The product of the same two numbers is . If the two numbers are each increased by one, the new product is . Find in terms of .
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
Example Question #1 : How To Use Foil In The Distributive Property
Expand the expression:
When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.
Example Question #6 : Distributive Property
Expand the following expression:
Or, written better
Example Question #7 : Distributive Property
Which of the following is equal to the expression ?
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
Example Question #2 : How To Use Foil In The Distributive Property
Simplify the expression.
None of the other answers
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.
Example Question #9 : Distributive Property
Given the equation above, what is the value of ?
Use FOIL to expand the left side of the equation.
From this equation, we can solve for , , and .
Plug these values into to solve.
Example Question #10 : Distributive Property
Expand and simplify the expression.
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.
Sum all of the terms and simplify. Do not forget the in front of the quadratic!
Finally, distribute the .