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We look at "X times X + 4" |
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| like any other multiplication. | ||
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| Just do X times X then X times 4 | ||
| and put the answers together. | ||
| We could even multiply (X + 4) times (X + 4) | ||
| Just multiply X + 4 times 4 | ||
| and then multiply X + 4 times X. | ||
| Then put the terms together in one place ... | ||
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| While it may be easy to see what's going on | ||
| writing the multiplication like this, | ||
| that's not the way it's usually written. | ||
| It's usually written all on one line. | ||
| We start like this ... | ||
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(X + 4)(X + 4) |
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| Take the first term in the first brackets | ||
| and multiply it by every term in the second bracket. | ||
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| Then take the second term in the first bracket | ||
| and multiply it by every term in the second bracket. | ||
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| Now we combine terms where we can. | ||
| An X 2 is not the same thing as an X. | ||
| We can't combine them. | ||
| We can combine the two different 4X terms we have. | ||
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(X + 4)(X + 4) = X2 + 4X + 4X + 16 = X2 + 8X + 16 |
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| The other way we did these problems was easier to follow, | ||
| but this way uses a lot less paper to write. | ||
| Math types love to save space, | ||
| so this is the way it is usually done. | ||
| More Examples: | ||
| (X - 5)(3X + 2) = 3X2 + 2X - 15X - 10 = 3X2 - 13X - 10 | ||
| (5X - 3)(X - 2) = 5X2 - 10X - 3X + 6 = 5X2 - 13X + 6 | ||
| (-X + 5)(2X + 4) = -2X2 - 4X + 10X + 20 = -2X2 + 6X + 20 | ||
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copyright 2005 Bruce Kirkpatrick |
