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: a^{2} - b^{2}
In the next two examples you can solve easily using the equation for a squared binomial pattern : a^{2}-2ab+b^{2}
Not, let's work out some equations:
1. Write out the sum and difference pattern: a^{2}-b^{2}
(x-2)(x+2)= x^{2}-2^{2}
Then you solve the equation:
=x^{2}-4
Now, Let's solve a squared binomial:
1. Write out the square of a binomial pattern: a^{2}+2ab+b^{2}
=(x+4)^{2}
= x^{2}+2(4)(x)+4^{2}
Then, solve the equation:
=x^{2}+8x+16
Here is one more square of a binomial equation:
(2x-5)^{2}
Write out the square of a binomial pattern: a^{2}+2ab+b^{2}
Substitute the equation numbers into the model equation:
4x^{2}+2(2x)(-5)+25
Solve the equation:
=4x^{2}-20x+25
As long as you follow the model equation for sum and difference patterns, a^{2}-b^{2}, and the model equation for square of a binomial pattern, a^{2}+2ab+b^{2}, it is extremely easy!
Related Links:
http://www.sosmath.com/algebra/factor/fac05/fac05.html
http://www.khanacademy.org/video/special-polynomials-products-1?playlist=Developmental%20Math
Source: Cite: Algebra 1, McDougal Littell Inc., 2001
Watch special polynomial problems get solved!
Source: Algebra 1, McDougal Littell Inc., 2001
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