5.5 The Product of Two Binomials
A binomial is a mathematical expression containing two terms.
There are four different types of products for binomials. We begin with number and write them then with variables:
A. (3 + 4) (3 - 5)
B. (3 - 4) (3 - 5)
C. (3 - 4) (3 + 5)
D. (3 + 4) (3 + 5)
Note that all the pairs of factors have a common term, in other words 3.
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We do the first multiplication: |
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3 |
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4 |
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3 |
- |
5 |
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-20 |
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- 15 |
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+ |
9 |
+12 |
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9 |
- 3 |
- 20 |
= - 14 |
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Check that it is correct:
(3 + 4) = 7
(3 - 5) = -2
7 · (-2) = - 14
It is correct!
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We will try to do an example with an algebraic expression, and we will replace the constant terms with variables, 3 with 1, 4 with b, and 5 with c. |
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a |
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b |
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a |
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c |
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- ac |
- bc |
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+ |
a2 |
+ ab |
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a2 + ab - ac |
- bc |
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a2 + a(b - c) |
- bc |
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