4.5 skm & pp 1 8.4 skm & pp 1 multiplying radical expressions
TRANSCRIPT
4.5 S KM & PP 18.4 S KM & PP 1
Multiplying Radical
Expressions
4.5 S KM & PP 28.4 S KM & PP 2
Notice!
Radical Expressions can be multiplied by using the Distributive
Property.
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The Distributive Propertyof Multiplication over
Addition and Subtraction
)cb(a
To multiply a monomial and a polynomial, multiply the
monomial with each term of the polynomial. This is the
DISTRIBUTIVE property.
)b(a )c(a
RECALL!
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FOIL using a Generic
Rectangle
)dc)(ba(
a bc
d
ac ad bc bd
ac
adbcbd
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Multiply Radicals
Basics
• Use Distributive Property to clear Parenthesis.•Simplify radicands using perfect square factors.
8.4 S
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The Distributive Property:
Example 1
)23(5 2535
1015
Final Answer:
1015
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Remember!
2
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MultiplyRadical Expressions
Example 2
)27(7 2777
1472
Final Answer:
147
147
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What Should We Do Here?
)25)(75(
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Recall! FOIL
Multiply each term of the first binomial with each term
of the second binomial.
)dc)(ba(
ac ad bc bd
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Example 3
)25)(75(
55 52 57 )2(7
14575252 1457525
)25)(75(
559
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Example 4
)2x)(7x(
xx x2 x7 )2(7
14x7x2x2 14x7x2x
)2x)(7x(
1455x
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Example 5
33 352 353 )52(5322 561531523
)5(61531523
)523)(533(
1527
)523)(533(
301531523
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Example 6
33 113 113 111122 111131133
1111113
2)113(
11214
)113)(113(
)113)(113(
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x+8 and x-8 areCONJUGATES
Let’s find their product!
)x)(x( 88
2x x8 64x8
642 x
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CONJUGATESLet’s find their
product!
)8x)(8x(
xx x8 64x8
64x
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CONJUGATESExample 7
)yx)(yx(
xx yx yyyx
22 yx
yx
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The Shortcut!
)ax)(ax(
22 ax
2x ax ax 2a
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The Shortcut:Example 8
)x)(x( 33 22 3x
92 x
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CONJUGATESThe Shortcut!
Example 9
)8x)(8x(
64x
22 )8()x(
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CONJUGATESExample 10
)yx)(yx(22 )y()x(
yx
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CONJUGATESExample 11
)11x)(11x(22 )11()x(
11x
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That’s All for Now!