Exponents
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PSAT Math › Exponents
Use FOIL to simplify the following product:
Explanation
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Explanation
The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:
Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.
Which of the following lists the above quantities from least to greatest?
I, IV, III, II
II, III, I, IV
I, III, II, IV
IV, III, II, I
I, IV, II, III
Explanation
If 
Cannot be determined
Explanation
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
Use FOIL to simplify the following product:
Explanation
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Simplify the radical expression.
Explanation
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
Simplify the radical expression.
Explanation
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
According to Heron's Formula, the area of a triangle with side lengths of a, b, and c is given by the following:
where s is one-half of the triangle's perimeter.
What is the area of a triangle with side lengths of 6, 10, and 12 units?
12√5
4√14
8√14
14√2
48√77
Explanation
We can use Heron's formula to find the area of the triangle. We can let a = 6, b = 10, and c = 12.
In order to find s, we need to find one half of the perimeter. The perimeter is the sum of the lengths of the sides of the triangle.
Perimeter = a + b + c = 6 + 10 + 12 = 28
In order to find s, we must multiply the perimeter by one-half, which would give us (1/2)(28), or 14.
Now that we have a, b, c, and s, we can calculate the area using Heron's formula.
Simplify:
Explanation
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 
According to Heron's Formula, the area of a triangle with side lengths of a, b, and c is given by the following:
where s is one-half of the triangle's perimeter.
What is the area of a triangle with side lengths of 6, 10, and 12 units?
12√5
4√14
8√14
14√2
48√77
Explanation
We can use Heron's formula to find the area of the triangle. We can let a = 6, b = 10, and c = 12.
In order to find s, we need to find one half of the perimeter. The perimeter is the sum of the lengths of the sides of the triangle.
Perimeter = a + b + c = 6 + 10 + 12 = 28
In order to find s, we must multiply the perimeter by one-half, which would give us (1/2)(28), or 14.
Now that we have a, b, c, and s, we can calculate the area using Heron's formula.