All PSAT Math Resources
Example Questions
Example Question #1 : How To Use Foil In The Distributive Property
Example Question #2 : How To Use Foil In The 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 #1 : 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 #1 : 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 #81 : Algebra
Expand the expression:
When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.
Example Question #3 : How To Use Foil In The Distributive Property
Expand the following expression:
Which becomes
Or, written better
Example Question #83 : Algebra
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 #84 : Algebra
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 #83 : Algebra
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 #85 : Algebra
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.
First:
Inside:
Outside:
Last:
Sum all of the terms and simplify. Do not forget the in front of the quadratic!
Finally, distribute the .