DISTRIBUTIVE PROPERTY AND POWER PROPERTIES

1
DISTRIBUTIVE PROPERTY AND POWER PROPERTIES

• You Control the Power!

2
Distributive Property

• Distribute a monomial over any polynomial
• Example 2x( 5x3 7x2 - 3x) ?
• Answer 10x4 14x3 - 6x2
• Next slide What if the first term is a
  binomial? Then repeat the process!

3
Distributive Property

• If the first expression has more than one term
  simply distribute each term through the entire
  second parentheses and then combine like terms
• Example (2x 6)( 5x3 7x2 - 3x) ?
• Answer
• 10x4 14x3 - 6x2 - 30x3 - 42x2 18x
• 10x4 - 16x3 - 48x2 18x

4
Distributive Property

• You try this one. Click to check your answer.
• Example (6a 5)( 2a3 - 3a2 - a) ?

5
Product of Powers Property

• When multiplying terms with the same base ? add
  the exponents
• Example x3 x5 x8
• When in doubt, stretch it out
• x3 x5 ? xxx xxxxx

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Quotient of Powers Property

• When dividing powers with the same base ?
  subtract the exponents
• (This has the same effect as cancelling.)
• Example
• When in doubt, stretch it out

7
Power of a Power Property

• When applying an exponent to an exponent ?
  multiply the exponents
• Example (x3)5 x15
• When in doubt, stretch it out
• (x3)5 ? (x3)(x3)(x3)(x3)(x3)
• ?xxx xxx xxx xxx xxx

8
Power of a Product Property

• When an exponent is applied outside a
  parenthetical product, it applies to each factor
  individually
• (Be careful not to call this distributive!)
• Example
• When in doubt, stretch it out

9
Power of a Quotient Property

• When an exponent is applied outside a quotient,
  it applies to each part individually
• Example
• When in doubt, stretch it out

10
Zero Power Property

• Any non-zero base to the zero power is equal to 1
• Examples x0 1 or 560 1
• Why should this be true? Quotient of Powers
  Property is one easy explanation.

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Zero Product Property

• If two factors have a product of zero, then one
  of those factors must equal zero.
• Example If xy 0, then x 0 or y 0.
• Why should this be true? How can you multiply
  two numbers and get zero for an answer?

12
Negative Power Property

• A negative power in the numerator, gets moved to
  the denominator.
• Examples
• Why should this be true? Quotient of Powers
  Property is one easy explanation.

13
Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

14
Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

15
Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

16
Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

17
Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

• 1 by the Zero Power Property

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Self Check find the answer and name the
property you used.-hit any key to reveal the
answer

• If (3x)(x 1) 0, then

• 3x 0 or x 1 0 by the
• Zero Product Property