Download The difference of two numbers is 5. Five times the lesser number

Chapter 7­1 Multiplying Polynomials
Word Problem: The difference of two numbers is 5. Five times the lesser number minus the greater number is 9. Write two equations to describe this linear system and find the two numbers.
Hint: both numbers are mixed numbers.
Homework: 7­1 Skills practice
1
2
Chapter 7­1 Multiplying Monomials Definition: a monomial is a number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. It has only one term.
Examples of monomials:
3
Which items below are monomials:
10
x + 3
2x2y
2x + 3x
4abcd
4xy ­ 5ab
x3y4z5
a2b­3c5
4 + 8
4
Product of Powers:
To multiply two powers that have the same base, add their exponents.
2+3 = x5
2 3
x ∙ x = x
Simplify (Always combine like terms first!)
(6n3) (2n7)
(r4)(­12r7)
(6cd5)(5c5d2)
5
Power of a Power:
To find the power of a power, multiply the exponents.
6
2 3 2∙3
(a ) = a = a
Simplify the following:
34
(x )
3 2 4 [(2 ) ]
232
[(3 ) ]
6
Power of a Product:
Find the power of each factor and multiply.
(ab)m = ambm
Example:
(­2xy3)5 = (­2)5x5(y3)5 = ­32x5y15
Simplify: [(8g3h4)2]2(2gh5)4
7
8
9
10
11