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. – 7:30 p.m.

Any questions from the homework that was due

today?(Section 5.2)

PleaseCLOSE

YOUR LAPTOPS,and turn off and put away your

cell phones,and get out your note-

taking materials.

Product Rule:am • an = am+n

Simplify each of the following expressions.

Example

32 • 34 = 36

x4 • x5 = x4+5

z3 • z2 • z5 = z3+2+5

(3y2)(-4y4) = 3 • y2 • -4 • y4 = (3 • -4)(y2 • y4) = -12y6

= 32+4

= x9

= z10

Review from section 5.1:

Power Rule:(am)n = amn

Example

Simplify each of the following expressions.

(23)3 = 29 = 512

(x4)2 = x8

= 23•3

= x4•2

More Review from section 5.1:

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) = (3 • -2)(x2 • x) = -6x3

(4x2)(3x2 – 2x + 5)= (4x2)(3x2) – (4x2)(2x) + (4x2)(5) (distributive property)

= 12x4 – 8x3 + 20x2 (multiply the monomials)

Multiply each of the following.

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework:

Example

(2x – 4)(7x + 5) = 2x(7x + 5) – 4(7x + 5)

= 14x2 + 10x – 28x – 20

= 14x2 – 18x – 20

Multiplying two BINOMIALS:

Use the distributive law two times:

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) = -10xInner: 3∙4x = 12xLast: 3∙(-5) = -15

FINAL ANSWER: 8x2 + 2x - 15

Try this in your notebook now with(3x – 5)(5x – 2):

We will come around and help if you have any questions.

Solution:

First: 3x∙5x = 15x2

Outer: 3x∙(-2) = -6xInner: -5∙5x = -25xLast: -5∙(-2) = +10

FINAL ANSWER: 15x2 - 31x + 10

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

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

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.

• Wednesdays– 10:10 am– 11:15 am

• Thursdays– 10:10 am– 11:15 pm

Gateway Quiz Retake Times(One new attempt allowed per week, beginning November 2)

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), to set up a date and time.

• Mondays– 1:25 pm– 2:30 pm

• Tuesdays– 1:25 pm– 3:35 pm