ma and pa math

Ma and Pa Math

Expanding Polynomials And

Common Factoring

Review

Expanding Polynomials• The product of two binomials can be found by multiplying EACH term in one binomial by EACH term in the other binomial• Then, simplify (collect like terms)

A B C D

Angelina and Brad go to the movies, where they meet Courtney and David.

If they were to all shake hands with the people they are just meeting…

who would shake hands with who?

A B C D

A B C D

A and C

A and D

B and C

B and D

Expanding polynomials works the same way!

Example 1: Expand and simplify.

a)

b)

3(x 2)

2y(y 1)

3x 6

In this case, the 2y is multiplied by y and the 2y is multiplied by 1.2y2 2y

In this case, the 3 ‘meets’ the x and the 3 ‘meets’ the 2.

c) (x 1)(x 4)

(2x 4)(3x 7y 8)d)

e) (x 4)(2x 3)(5x 1)

Common Factoring•When factoring polynomial expressions, look at both the numerical coefficients and the variables to find the greatest common factor (G.C.F.)• Look for the greatest common numerical factor and the variable with the highest degree of the variable common to each term•To check that you have factored correctly, EXPAND your answer (because EXPANDING is the opposite of FACTORING!)

Example 2: Factor.a)

b)

c)

2x2 8x

9x2y 3xy2

12m3n2 6m4n3 4m2n5 2m2n2

Exponent Laws

Radicals!

Radicals and Exponents•A radical is a root to any degree

E.g. is a squared root, is a cubed root.

• A repeated multiplication of equal factors (the same number) can b expressed as a power

Example: 3 x 3 x 3 x 3 = 34 34 is the power 3 is the base 4 is the exponent

Radicals and Exponents

53 = “5 to the three”

64 = “six to the four”

Hizzo = “H to the Izzo”

Radicals and Exponents

63 = 6 x 6 x 6

Radicals and Exponents

52 x 55

= (5 x 5) x (5 x 5 x 5 x 5 x 5)

= 57

Radicals and Exponents

68 65 = = = 63

Radicals and Exponents

= (72) x (72) x (72)

= (7 x 7) x ( 7 x 7) x (7 x 7)

= (7 x 7) x ( 7 x 7) x (7 x 7)

= 76

Radicals and Exponents

= (3 x 2) x ( 3 x 2) x (3 x 2) x (3 x

2)

= (3 x 3 x 3 x 3) x (2 x 2 x 2 x 2)

= (34) x (24)

Radicals and Exponents

= x x

=

=

The Power of Negative Numbers

• There is a difference between –32 and (–3)2

• The exponent affects ONLY the number it touches

So, –32 = –(3 x 3), but (–3)2 = (–3) x (–3) = –9 = 9

Homework

p. 399 # 1 – 3, 5 – 11 (alternating!)

Challenge

Pg. 401 #16 – 18