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Example Questions
Example Question #4 : How To Find Excluded Values
Find the extraneous solution for
There are no extraneous solutions
Now lets plug these values into our original equation.
For
So this isn't an extraneous solution.
For
Since ,
is an extraneous solution.
Example Question #2671 : Sat Mathematics
Example Question #2672 : Sat Mathematics
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 #2673 : Sat Mathematics
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 #3 : Foil
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 #2674 : Sat Mathematics
Expand the expression:
When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.
Example Question #2675 : Sat Mathematics
Expand the following expression:
Which becomes
Or, written better
Example Question #2676 : Sat Mathematics
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 #2677 : Sat Mathematics
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 #2678 : Sat Mathematics
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.
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