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4.6a S KM & PP 1
Polynomial Multiplication:
Product of Conjugates
4.6a S KM & PP 2
What are Conjugates?
ba
ba
The first binomial is the sum of a and b. The conjugate binomial is the difference of a and b.
4.6a S KM & PP 3
Let’s Look at some Examples!
Binomial Conjugate
5x 5x8x 8x
12 x 12 x3 x 3 x73 x 73 x
4.6a S KM & PP 4
Expression Conjugate
Will there be more conjugates in Algebra
?
Yes. Have a look at a couple examples that come up in more advanced sections:
273 x 273 x
i54 i54
4.6a S KM & PP 5
The Product of Conjugates
Use FOIL to multiply these conjugates.
)ax)(ax( 2x ax ax 2a
22 ax
4.6a S KM & PP 6
FOIL Conjugatesusing a Generic
Rectangle
)ax)(ax(
x a
xa
2xax
ax2a
2x ax ax 2a22 ax
4.6a S KM & PP 7
The Shortcut!
)ax)(ax(
22 ax
2x ax ax 2a
4.6a S KM & PP 8
The Shortcut:Example 1
)x)(x( 33 22 3x
92 x
4.6a S KM & PP 9
The Shortcut:Example 2
)x)(x( 77 22 7x
492 x
4.6a S KM & PP 10
The Shortcut:Example 3
)x)(x( 5252
22 52 x
254 2 x
4.6a S KM & PP 11
The Shortcut:Example 4
)x)(x( 6767
22 67 x
3649 2 x
4.6a S KM & PP 12
The Shortcut:Example 5
)x)(x( 112112
22 112 x
1144 2 x
4.6a S KM & PP 13
The Shortcut:Example 6
)yx)(yx( 9494
22 94 yx 22 8116 yx
4.6a S KM & PP 14
Memorize this Pattern
for now and for later!
)ax)(ax( 22 ax In a future section, we will need to work this problem
in reverse. We will be given the difference of
squares and must rewrite it as a product of
conjugates. It will look like this: )x)(x( 33 92x
4.6a S KM & PP 15
That’s All for Now!