Polynomials are algebraic expressions involving variables and their powers. The degree of a polynomial is the highest power of the variable. To add or subtract polynomials, like terms must be combined. To multiply polynomials, the distributive property and FOIL method are used. Special formulas exist for multiplying the sum and difference of expressions.

1. Algebraic Expressions

2. Polynomials
 A polynomial is an expression in the form:
anxn+an-1xn-1+…+a1x+a0
 Example: x2+5x+6
 The degree of a polynomial is the highest
power of the variable that appears in the
polynomial.
 For example:
2x2-3x+4 (Has degree of 2)
x8+5x (Has degree of 8)

3. Combining Algebraic
Expressions
 To add and subtract polynomials, you must
use the properties of real numbers.
 Quick Review
 Commutative Property:
a+b=b+a
ab = ba
 Associative Property:
(a + b) + c = a + (b + c)
(ab)c = a(bc)
 Distributive Property:
a(b + c) = ab + ac
(b + c)a = ab + ac

4. Adding Polynomials
➲ In order to add or subtract polynomials, you
must collect like terms.
➲ For example:
(x3-6x2+2x+4)+(x3+5x2-7x)
=(x3+x3)+(-6x2+5x2)+(2x-7x)+4 Group like terms
=2x3-x2-5x+4

5. Subtracting Polynomials
➲ In order to subtract polynomials, you must first use the
distributive property.
➲ For Example,
 (x3-6x2+2x+4)-(x3+5x2-7x)
 x3-6x2+2x+4-x3-5x2+7x
 (x3-x3)+(-6x2-5x2)+(2x+7x)+4
 -11x2+9x+4

6. Multiplying Algebraic
Expressions
• You can multiply two algebraic expressions
using the Distributive Property and the Laws of
Exponents.
• Recall: aman = am+n
• The acronym FOIL can help you to remember
that the product of two binomials is the sum of
the products of the First terms, the Outer
terms, the Inner terms, and the Last terms.

7. Multiplying Algebraic
Expressions
➲ Example:
(2x+1)(3x-5)
=6x2-10x+3x-5

8. Special Product Formulas
➲ If A and B are any real numbers or algebraic
expressions, then:
➲ 1. (A+B)(A-B) = A2 – B2 Sum and product of same terms
➲ 2. (A+B)2 = A2 + 2AB + B2 Square of a sum
➲ 3. (A-B)2 = A2 – 2AB + B2 Square of a difference
➲ 4. (A+B)3 = A3+3A2B+3AB2+B3 Cube of a sum
➲ 5. (A-B)3 = A3-3A2B+3AB2-B3 Cube of a difference