# Coming up: - PowerPoint PPT Presentation

1 / 19

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!.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Coming up:

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### 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 four weeks left in the semester, including finals week.

### Any questions on the Section 5.3 homework?

CLOSE

and turn off and put away your cell phones,

and get out your note-taking materials.

### Section 5.4More 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

= y2 – 8y – 48

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

F O I L

y2 + 4y – 12y – 48

(y – 12)(y + 4) =

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.

Multiply (3x + 4)2

Remember that a2 = a• a, so (3x + 4)2 = (3x + 4)(3x + 4).

Example

(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 !!!

Problem from today’s homework:

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

= a2 – 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:

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, or email Krystle at mayerkr@uwstout.edu.

### 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. – 7:30 p.m.

This lab is closed on Fridays,

on weekends and during breaks.

• Mondays:

• 1:25 pm

• 2:30 pm

• Tuesdays:

• 12:20 pm

• 1:25 pm

• Wednesdays:

• 10:10 am

• 11:15 am

• Thursdays:

• 10:10 am

• 11:15 am