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Precalculus: Chapter P Homework Notes
Precalculus: Chapter P Homework Notes
28
Mathematics
Undergraduate 1
11/30/2015
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Term
What Symbols does Inequality Notation Utilize?
 Definition
>,
<,
Greater than or Equal To,
Less Than or Equal To
Term
How Does Interval Notation Work?
 Definition
Parenthesis are used for numbers that are greater than or less than.

Brackets are used for numbers that are greater than or equal to and numbers that are less than or equal to.

Numbers within the brackets and parenthesis are listed in order from least to greatest.
Term
Write The Following in Interval Notation:
x is less than three and greater than or equal to two.
 Definition
[2,3)
Term
How to Subtract Two Fractions?
 Definition
1.) (a/b)-(c/d)
2.) Set it as an addition problem
(a/b)+(-c/d)
3.) Multiply by least common denominator
(ad/-bd)+(-cb/bd)
4.) Simplify
Term
How to Divide Fractions?
 Definition
1.)(a/b)/(c/d)
2.) Change it into a multiplication problem by multiplying the first fraction by the reciprocal of the second fraction
(a/b)*(d/c)
3.) Multiply the numerator of the first fraction by the numerator of the second fraction, and multiply the denominator of the first fraction by the denominator of the second fraction
(ad/bc)
Term
What is the Product Rule of Exponents?
 Definition
(a^b)*(a^c)=a^(b+c)
Term
What is the Power Rule of Exponents?
 Definition
(a^b)^c=a^(bc)
Term
What is the negative rule of exponents?
 Definition
a^-b=1/a^b
Term
What is the Quotient Rule of Exponents?
 Definition
a^b/a^c=(a^(b-c))
Term
How do You Square a Binomial?
 Definition
Case One: (A+B)^2=A^2+2AB+B^2
Case Two: (A-B)^2=A^2-2AB+B^2
Term
How to Reduce a Rational Expression to Lowest Terms?
 Definition
1.) Factor the numerator
2.) Factor the denominator
3.) Remove the common factors in the numerator and denominator
Term
How to find all the values that must be excluded from a rational expression?
 Definition
1.) Find all values of the variable that would make the expression equal zero
2.) The variable cannot equal those numbers.
Term
How do you multiply rational expressions in the form of?:

(ax-b/cx+d)*(ex-f/gx-h)
 Definition
1.)Set the two rational expressions being multiplied together as one rational expression by multiplying the numerators and denominators together.
2.) Factor the numerator
3.) Factor the denominator
4.) Remove the common factors
5.) Simplify
Term
How to Subtract Terms That Are Square Roots?
 Definition
1.) Simplify Each Term
2.) Then Subtract Them
Term
a^1/b=
 Definition
the b root of a to the power of 1
Term
(a^b)(a^c)=
 Definition
a^(b+c)
Term
How to add fractions?
 Definition
1.)(a/b)+(c/d)
2.)Multiply by least common denominator
(ad/bd)+(cb/bd)
3.)Simplify
Term
A^2-B^2=
 Definition
(A-B)(A+B)
Term
A^3-B^3=
 Definition
(A-B)(A^2+AB+B^2)
Term
A^3+B^3=
 Definition
(A+B)(A^2-AB+B^2)
Term
A/B*C/D=
 Definition
A*C/B*D
Term
(A/B)/(C/D)=
 Definition
(A*D)/(B*C)
Term
a^(b/c)=
 Definition
c root of a to the power of b
Term
The absolute value of a is equal to...
 Definition
the squareroot of a^2
Term
n root of a equals b is equal to
 Definition
b^n=a
Term
(A/B)+(C/D)=
 Definition
AD-BC/BD
Term
(A/B)-(C/D)=
 Definition
AD+BC/BD
Term
a(b+c)=
 Definition
ab+ac
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