Reminders

1
Reminders

• Homework 7.5Due Fri Night
• Final Wednesday the 12th 8-10

2
More Examples

• (4x 3)(2x 4)
• 3w(w 2)
• q4(q8)
• -6x9(-2x2)
• 3p2q(4p2 pq 2q2)
• (2x 7y)(3x 2y)
• (-3a2 5b2)(2a2 3b2)

3
Section 7.5Powers of Polynomials
4
Objective

• Today we will continue to work with monomials
  with exponents and today we will add raising a
  monomial to a power.

5
Questions

• What do we do when we add polynomials?
• What do we do when we subtract polynomials?
• What do we do when we multiply polynomials?

6
More Questions

• When multiplying variables what do we do with the
  coefficients, what do we do with the exponents?
• What method can we use to multiply two binomials?
• When will the FOIL method not work? What do we
  do in this case?

7
Raising a monomial to a power

• Write out what (4w)3 means.
• (4w)3 (4w) (4w) (4w)
• 4 w 4 w 4 w
• 4 4 4 w w w
• 64w3

8
General Rule

• This could be annoying to write out if we raise a
  monomial to a large power. i.e. (4xy)17
• When raising a MONOMIAL to a power we can use the
  following rule
• (xy)n xnyn
• REMBER this only works with monomials
• ie (x y)n is simplified and cannot be written
  in another form

9
Examples

• (6zm)3
• (4mn)6
• (-3y)4
• (-7x)3

10
Raising a binomial to a power

• When raising a binomial to a power we will be
  raising it only to a second power.
• First rewrite the expression to get rid of the
  exponent.
• Then use the FOIL method to solve.

11
Raising a binomial to a power

• Examples
• (4x 3)2
• (4x 3)2
• (10 6x)2
• (3x 5y)2

12
Raising a binomial to a power

• Can we make any general-izations in our answers?
• 16x2 24x 9 (4x)2 24x3 (3)2
• 16x2 - 24x 9
• 100 120x 36x2
• 9x2 30xy 25y2

13
General Rule

• When squaring a binomial we know it should be in
  this form
• (A B)2 A2 2(AB) B2
• You dont need to know this general form to
  calculate the product of two binomials but it may
  be a good way to check your answer.
• This General formula also comes in handy when
  factoring binomials.

14
Special Cases

• Lets look at some products of binomials.
• (3x 4)(x 4)
• (2x 5)(2x 5)
• (x y)(4x y)
• (7x 3)(7x 3)

15
Special Cases

• So notice that the last example looks different
  than the rest.
• So if we have two binomials that are identical
  except one is addition and the other is
  subtraction we call the two terms Binomial
  Conjugates.

16
General Rule

• This only works if we have two binomials that are
  identical except one is addition and the other is
  subtraction
• (A B)(A B) A2 B2
• We call A2 B2 the Difference of Two Squares

17
Exit Task 7.4

• Simplify
• a)
• b)
• c)
• d)

18
Exit Task 7.4

• Simplify
• a) (2x 7y)(3x 2y)
• b) (5x 6)2
• c) (2x 7)(2x 7)
• d) (3t2 3t 4)(2t2 1)