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)

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Product Rule: a m a n = a m+n Simplify each of the following expressions. Example = 3 6 x 4 x 5 = x 4+5 z 3 z 2 z 5 = z (3y 2 )(-4y 4 )= 3 y 2 -4 y 4 = (3 -4)(y 2 y 4 )= -12y 6 = = x 9 = z 10 Review from section 5.1:

Power Rule: (a m ) n = a mn Example Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 33 = x 42 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: (3x 2 )(-2x)= (3 -2)(x 2 x)= -6x 3 (4x 2 )(3x 2 – 2x + 5) = (4x 2 )(3x 2 ) – (4x 2 )(2x) + (4x 2 )(5) (distributive property) = 12x 4 – 8x x 2 (multiply the monomials) Multiply each of the following.

Problem from today’s homework:

Example (2x – 4)(7x + 5)= 2x(7x + 5) – 4(7x + 5) = 14x x – 28x – 20 = 14x 2 – 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 = 8x 2 Outer: 2x∙(-5) = -10x Inner: 3∙4x = 12x Last: 3∙(-5) = -15 FINAL ANSWER: 8x 2 + 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 = 15x 2 Outer: 3x∙(-2) = -6x Inner: -5∙5x = -25x Last: -5∙(-2) = +10 FINAL ANSWER: 15x x + 10

Example Multiply (3x – 7y)(7x + 2y) (3x – 7y)(7x + 2y)= (3x)(7x + 2y) – 7y(7x + 2y) = 21x 2 + 6xy – 49xy – 14y 2 = 21x 2 – 43xy –14y 2

Problem from today’s homework:

Example Multiply (3x + 4) 2 Remember that a 2 = a a, so (3x + 4) 2 = (3x + 4)(3x + 4). (3x + 4) 2 = (3x + 4)(3x + 4)= (3x)(3x + 4) + 4(3x + 4) = 9x x + 12x + 16 = 9x x + 16

Example Multiply (5x – 2z) 2 (5x – 2z) 2 = (5x – 2z)(5x – 2z)= (5x)(5x – 2z) – 2z(5x – 2z) = 25x 2 – 10xz – 10xz + 4z 2 = 25x 2 – 20xz + 4z 2

Problem from today’s homework:

Example Multiply (a + 2)(a 3 – 3a 2 + 7). (a + 2)(a 3 – 3a 2 + 7) = a(a 3 – 3a 2 + 7) + 2(a 3 – 3a 2 + 7) = a 4 – 3a 3 + 7a + 2a 3 – 6a = a 4 – a 3 – 6a 2 + 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… 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