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When you learn how to recognize the special product polynomials quickly and easily, you can solve them a lot faster.
(x-2)(x+2)--- are there any patterns?
(x+5)2--- any patterns here?
(x-6)2--- how about here?
In the first example, you can cancel out the last two number using the equation for a sum and difference pattern: a2 - b2
In the next two examples you can solve easily using the equation for a squared binomial pattern : a2-2ab+b2
Not, let's work out some equations:
1. Write out the sum and difference pattern: a2-b2
Then you solve the equation:
Now, Let's solve a squared binomial:
1. Write out the square of a binomial pattern: a2+2ab+b2
Then, solve the equation:
Here is one more square of a binomial equation:
Write out the square of a binomial pattern: a2+2ab+b2
Substitute the equation numbers into the model equation:
Solve the equation:
As long as you follow the model equation for sum and difference patterns, a2-b2, and the model equation for square of a binomial pattern, a2+2ab+b2, it is extremely easy!
Source: Cite: Algebra 1, McDougal Littell Inc., 2001
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Source: Algebra 1, McDougal Littell Inc., 2001