Coming up:
• Today:
Section 5.4
• Next class:
Section 5.6 (last new section!)
• Next two class days after that:
•
•
Review for Quiz 3
Quiz 3 on sections 5.1-5.4 and 5.6
Gateway Quiz Reminder!
If you have not passed your gateway quiz
yet, remember to come in, review the
last one you took, and sign up to take
the next version.
After this week there are just three weeks
left in the semester, including finals
week.
Any questions on
the Section 5.3
homework?
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Section 5.4
More on Multiplying Polynomials
Review from last section:
When multiplying 2 binomials, the distributive
property can be easily remembered as the
FOIL method.
F – product of First terms
O – product of Outside terms
I – product of Inside terms
L – product of Last terms
Example
Multiply (y – 12)(y + 4)
(y – 12)(y + 4)
Product of First terms is y2
(y – 12)(y + 4)
Product of Outside terms is 4y
(y – 12)(y + 4)
Product of Inside terms is -12y
(y – 12)(y + 4)
Product of Last terms is -48
(y – 12)(y + 4) =
F O
I
L
y2 + 4y – 12y – 48
= y2 – 8y – 48
In the process of using the FOIL method on
products of certain types of binomials, we see
specific patterns that lead to special products.
Examples: Squaring a Binomial
• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
Note: These might be just as easy to do by the
usual FOIL method, which is what we will
demonstrate in class, rather than by
memorizing these formulas.
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
EXTREMELY IMPORTANT NOTE:
(3x + 4)2 is NOT simply (3x)2 + 42 !!!
Example
Multiply (5x – 2z)2
(5x – 2z)2 = (5x – 2z)(5x – 2z) = (5x)(5x – 2z) – 2z(5x – 2z)
= 25x2 – 10xz – 10xz + 4z2
= 25x2 – 20xz + 4z2
REMINDER:
(5x -2z)2 is NOT simply (5x)2 – (2z)2 !!!
Another special products pattern is seen when
multiplying the sum and difference of two terms
such as (a + b)(a – b) .
By the FOIL method:
(a + b)(a – b)
= a ∙a + a ∙(-b) + a ∙b + b ∙(-b)
= a2 – ab + ab – b2
= a 2 – b2
Recognizing this pattern can save you some time, since the
middle terms will always cancel each other out.
(a + b)(a – b) = a2 – b2
Problem from today’s homework:
Problem from today’s homework:
Problem from today’s homework:
Reminders:
Next class session:
HW 5.4 due at start of class
Don’t forget to take this week’s
Gateway in the open lab if you
haven’t yet scored 8/8.
Sign up for a time with a TA in the open
lab next door!
Math TLC Open Lab Hours:
Room 203 Jarvis Hall Science Wing
(next door to the JHSW 214 Math TLC classroom)
Monday through Thursday
8:00 a.m. – 6:30 p.m.
This lab is closed on Fridays,
on weekends and during breaks.
Gateway Quiz Retake Times
(One new attempt allowed per week,
beginning March 7)
• Mondays
• Wednesdays
– 1:25 pm
– 2:30 pm
– 10:10 am
– 11:15 am
• Tuesdays
• Thursdays
– 10:10 am
– 11:15 am
– 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.
You may now
OPEN
your LAPTOPS
and begin working on the
homework assignment.