Tutorial

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

Our College Algebra Course is only $329.

Sophia's online courses not only save you money, but credits are also eligible for transfer to over 2,000 colleges and universities.*

*The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 16 of Sophia's online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.