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.
4.5 S KM & PP 3
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!
4.5 S KM & PP 4
FOIL using a Generic
Rectangle
)dc)(ba(
a bc
d
ac ad bc bd
ac
adbcbd
KM & PP 5
Multiply Radicals
Basics
• Use Distributive Property to clear Parenthesis.•Simplify radicands using perfect square factors.
8.4 S
4.5 S KM & PP 6
The Distributive Property:
Example 1
)23(5 2535
1015
Final Answer:
1015
4.5 S KM & PP 78.2 S KM & PP 7
Remember!
2
4.5 S KM & PP 8
MultiplyRadical Expressions
Example 2
)27(7 2777
1472
Final Answer:
147
147
4.5 S KM & PP 9
What Should We Do Here?
)25)(75(
4.5 S KM & PP 10
Recall! FOIL
Multiply each term of the first binomial with each term
of the second binomial.
)dc)(ba(
ac ad bc bd
4.5 S KM & PP 11
Example 3
)25)(75(
55 52 57 )2(7
14575252 1457525
)25)(75(
559
4.5 S KM & PP 12
Example 4
)2x)(7x(
xx x2 x7 )2(7
14x7x2x2 14x7x2x
)2x)(7x(
1455x
4.5 S KM & PP 13
Example 5
33 352 353 )52(5322 561531523
)5(61531523
)523)(533(
1527
)523)(533(
301531523
4.5 S KM & PP 14
Example 6
33 113 113 111122 111131133
1111113
2)113(
11214
)113)(113(
)113)(113(
4.5 S KM & PP 15
x+8 and x-8 areCONJUGATES
Let’s find their product!
)x)(x( 88
2x x8 64x8
642 x
4.5 S KM & PP 16
CONJUGATESLet’s find their
product!
)8x)(8x(
xx x8 64x8
64x
4.5 S KM & PP 17
CONJUGATESExample 7
)yx)(yx(
xx yx yyyx
22 yx
yx
4.5 S KM & PP 18
The Shortcut!
)ax)(ax(
22 ax
2x ax ax 2a
4.5 S KM & PP 19
The Shortcut:Example 8
)x)(x( 33 22 3x
92 x
4.5 S KM & PP 20
CONJUGATESThe Shortcut!
Example 9
)8x)(8x(
64x
22 )8()x(
4.5 S KM & PP 21
CONJUGATESExample 10
)yx)(yx(22 )y()x(
yx
4.5 S KM & PP 22
CONJUGATESExample 11
)11x)(11x(22 )11()x(
11x
4.5 S KM & PP 238.4 S KM & PP 23
That’s All for Now!