DISTRIBUTIVE PROPERTY AND POWER PROPERTIES You Control the

DISTRIBUTIVE PROPERTY AND POWER PROPERTIES You Control the Power!

Distributive Property • Distribute a monomial over any polynomial: • Example: 2 x( 5 x 3 + 7 x 2 - 3 x) = ? • Answer: 10 x 4 + 14 x 3 - 6 x 2 • Next slide: What if the first term is a binomial? Then repeat the process!

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: (2 x – 6)( 5 x 3 + 7 x 2 - 3 x) = ? • Answer: 10 x 4 + 14 x 3 - 6 x 2 - 30 x 3 - 42 x 2 + 18 x 10 x 4 - 16 x 3 - 48 x 2 + 18 x

Distributive Property • You try this one. Click to check your answer. • Example: (6 a – 5)( 2 a 3 - 3 a 2 - a) = ? • Answer: 12 a 4 – 18 a 3 – 6 a 2 – 10 a 3 + 15 a 2 + 5 a 12 a 4 – 28 a 3 + 9 a 2 + 5 a

Product of Powers Property • When multiplying terms with the same base add the exponents • Example: x 3 x 5 = x 8 • When in doubt, stretch it out: x 3 x 5 xxxxx

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:

Power of a Power Property • When applying an exponent to an exponent multiply the exponents • Example: (x 3)5 = x 15 • When in doubt, stretch it out: (x 3 )5 (x 3 )(x 3 ) xxx xxx xxx

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:

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:

Zero Power Property • Any non-zero base to the zero power is equal to 1 • Examples: x 0 = 1 or 560 = 1 • Why should this be true? Quotient of Powers Property is one easy explanation.

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?

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.

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • • by the Product of Powers Property

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • • by the Power of a Power Property

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • • by the Quotient of Powers Property

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • • by the Negative Power Property

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • • =1 by the Zero Power Property

Self Check: find the answer and name the property you used. -hit any key to reveal the answer • If (3 x)(x – 1) = 0, then • 3 x = 0 or x – 1= 0 by the Zero Product Property