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
(x-2)(x+2)= x2-22
Then you solve the equation:
=x2-4
Now, Let's solve a squared binomial:
1. Write out the square of a binomial pattern: a2+2ab+b2
=(x+4)2
= x2+2(4)(x)+42
Then, solve the equation:
=x2+8x+16
Here is one more square of a binomial equation:
(2x-5)2
Write out the square of a binomial pattern: a2+2ab+b2
Substitute the equation numbers into the model equation:
4x2+2(2x)(-5)+25
Solve the equation:
=4x2-20x+25
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!
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