REMINDER:
You must pass the Gateway to pass this class, regardless of your
grades in the online work, so plan ahead to put in the necessary
review time in the tutor lab so you can get this hurdle jumped well
before finals week.
(You can find more practice quizzes online in the Gateway Info menu
area, or get additional paper copies in the open lab.)
There are 4 weeks left in the semester
after this week, including finals week.
Math TLC Open Lab Hours:
Room 203
Jarvis Hall Science Wing
Monday through Thursday
8:00 a.m. – 6:30 p.m.
Any questions from the
homework that was due
today?
(Section 5.2)
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Review from section 5.1:
Product Rule:
am • an = am+n
Example
Simplify each of the following expressions.
32 • 34 = 32+4 = 36
x4 • x5 = x4+5 = x9
z3 • z2 • z5 = z3+2+5 = z10
(3y2)(-4y4) = 3 • y2 • -4 • y4 = (3 • -4)(y2 • y4) = -12y6
More Review from section 5.1:
Power Rule:
(am)n = amn
Example
Simplify each of the following expressions.
(23)3 = 23•3 = 29 = 512
(x4)2 = x4•2 = x8
Section 5.3
• Multiplying polynomials
• If all of the polynomials are monomials, use the
associative and commutative properties.
• If any of the polynomials are not monomials,
use the distributive property before the
associative and commutative properties. Then
combine like terms.
Examples:
(3x2)(-2x)
Multiply each of the following.
= (3 • -2)(x2 • x) = -6x3
(4x2)(3x2 – 2x + 5)
= (4x2)(3x2) – (4x2)(2x) + (4x2)(5)
= 12x4 – 8x3 + 20x2
(distributive property)
(multiply the monomials)
Problem from today’s homework:
Problem from today’s homework:
Problem from today’s homework:
Example
Multiplying two BINOMIALS:
Use the distributive law two times:
(2x – 4)(7x + 5) = 2x(7x + 5) – 4(7x + 5)
= 14x2 + 10x – 28x – 20
= 14x2 – 18x – 20
A note about the last example:
One way to remember all of the steps when you multiply a
BINOMIAL times a BINOMIAL is called the “FOIL” method:
F = First (multiply the two first terms together)
O = Outer (multiply the two outer terms together)
I = Inner (multiply the two inner terms together)
L = Last (multiply the two last terms together)
Example
(2x + 3)(4x – 5):
Solution:
First: 2x∙4x = 8x2
Outer: 2x∙(-5) = -10x
Inner: 3∙4x = 12x
Last: 3∙(-5) = -15
FINAL ANSWER:
8x2 + 2x - 15
Example
Multiply (3x – 7y)(7x + 2y)
(3x – 7y)(7x + 2y) = (3x)(7x + 2y) – 7y(7x + 2y)
= 21x2 + 6xy – 49xy – 14y2
= 21x2 – 43xy –14y2
Problem from today’s homework:
Example
Multiply (3x + 4)2
Remember that a2 = a • a, so (3x + 4)2 = (3x + 4)(3x + 4).
(3x + 4)2 = (3x + 4)(3x + 4) = (3x)(3x + 4) + 4(3x + 4)
=
9x2 + 12x + 12x + 16
=
9x2 + 24x + 16
Problem from today’s homework:
Example
Multiply (a + 2)(a3 – 3a2 + 7).
(a + 2)(a3 – 3a2 + 7) = a(a3 – 3a2 + 7) + 2(a3 – 3a2 + 7)
=
a4 – 3a3 + 7a + 2a3 – 6a2 + 14
=
a4 – a3 – 6a2 + 7a + 14
Don’t forget:
This assignment is due by start
of next class period.
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning March 7)
• Mondays
– 1:25 pm
– 2:30 pm
• Tuesdays
– 10:10 am
– 11:15 am
• Wednesdays
– 10:10 am
– 11:15 am
• Thursdays
– 1:25 pm
– 2:30 pm
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you…
email Krystle Mayer, Math TLC Coordinator (JHSW 201) or Dr.
Laura Schmidt, to set up a date and time.