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Algebra 6 Point 10
1.
2.
To find products
of the form (a + b)(a â b)Frameworks: 10.P.3
3.
How do we
square a binomial? (x + 3)2 = (x + 3)(x + 3) FOIL: = x2 + 3x + 3x + 9 = x2 + 6x + 9 Square of a sum: (first term)2 + 2(first x last) + (last term)2
4.
Squaring a difference:
(3x - 5)2 = (3x - 5)(3x - 5) FOIL: = 9x2 - 15x - 15x + 25 = 9x2 - 30x + 25 Square of a difference: (first term)2- 2(first x last) + (last term)2
5.
Notice (x +
3)2 â x2 + 9 (3x â 5)2â 9x2+ 25 When you square a binomial the product always contains three terms.
6.
Square of a
Binomial (a + b)2 = a2+ 2ab + b2 (a - b)2 = a2- 2ab + b2
7.
Try some: (x
â 8)(x - 8) (2y + 1)2 (3x - 2)2 (5a + 1)2
8.
What about multiplying
the sum and difference of the same 2 terms? (x + 6)(x - 6) FOIL: = x2 - 6x + 6x - 36 = x2 - 36 (first term)2 - (last term)2 Product of (a + b)(a â b): a2- b2
9.
Try some: (c
â 1)(c + 1) (4x â 3)(4x + 3) (3x + 2)(3x â 2)
10.
And now for
something really fun: (x â 5)2 = (x -8)(x + 8) x2â 10x + 25 = x2 â 64 - x2 = -x2 â 10x + 25 = â 64 - 25 - 25 - 10 x = - 89 x = 8.9
11.
Try another fun
one: (x â 4)2 = (x -8)(x + 2)
12.
Turn to page
234 Do 1-4
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