ACT Math : Algebra
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Example Questions
Example Question #2581 : Act Math
When subtracting matrices, subtracting component-wise.
Example Question #1 : How To Subtract Matrices
If 
15
3
12
26
0
15
Match each term from the first matrix with the corresponding number from the second matrix and subtract.
Simplify.
Each of the numbers in the matrix solution now corresponds to the letters, a through f. Add a (upper left) and f (lower right).
Example Question #1 : How To Find Combinations With A Matrix
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter 
Example Question #1 : Matrix Combinations
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Example Question #1093 : Algebra
At a sale, a necklace that was originally 
Taking ten percent off of 
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of 
Example Question #1 : Foil
For all x, (4x – 3)2 =
12x2 + 24x – 9
16x2 – 24x + 9
16x2 + 24x + 9
16x2 + 9
16x2 – 9
16x2 – 24x + 9
To solve this problem, you should FOIL: (4x – 3)(4x – 3) = 16x2 – 12x – 12x + 9 = 16x2 – 24x + 9.
Example Question #1 : Distributive Property
Which of the following is equivalent to (2g – 3h)2?
4g2 + 9h2
4g2 – 12gh + 9h2
4g2 – 6gh + 9h2
4g2 – 12gh + 3h2
g2 – 12gh + 9h2
4g2 – 12gh + 9h2
Use FOIL: (2g – 3h)(2g – 3h) = 4g2 – 6gh – 6gh + 9h2 = 4g2 – 12gh + 9h2
Example Question #2 : Distributive Property
Use FOIL on the following expression:
x(x + 1)(x – 1)
x3 – x2
x
x – 1
x3 – x
x2 – x
x3 – x
FOIL (First, Outside, Inside, Last): (x + 1)(x – 1) which is (x2 – 1) then multiply it by x, which is (x3 – x)
Example Question #1 : Foil
Multiply: (4x + 3)(2x + 4)
8x² + 34
6x² + 16x + 24
8x² + 22x +12
30x + 12
3x² + 12x – 12
8x² + 22x +12
To solve you must use FOIL (first outer inner last)
Multiply 4x and 2x to get 8x²
Multiply 4x and 4 to get 16x
Multiply 3 and 2x to get 6x
Multiply 3 and 4 to get 12
Add the common terms and the awnser is 8x² + 22x + 12
Example Question #2 : Distributive Property
What is the greatest common factor in the evaluated expression below?
This is essentially a multi-part question that at first may seem confusing, until it's realized that the question only involves basic algebra, or more specifically, using FOIL and greatest common factor concepts.
First, we must use FOIL (first, outside, inside, last), to evaluate the given expression: ⋅
First:
Outside:
Inside:
Last:
Now add all of the terms together:
Which simplifies to:
Now, we must see what is greatest common factor shared between each of these two terms. They are both divisible by 
Therefore, 
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