somebody please explain factoring to me

Algebra
Tutor: None Selected Time limit: 1 Day

studying for my g.e.d. and need factoring explained to me, please show me how to solve this in detail: 3c^2de^2+6cde^2+3de^2

Apr 15th, 2015

First compare the coefficients 3, 6, and 3. They have the common factor 3 and this is the greatest common factor (gcf) for them. Then look at the letters in the expressions 3c^2de^2, 6cde^2, and 3de^2. c is not present in in the third term, so it will not be present in the gcf. The smallest power of d for these three terms is d (or d^1) and the smallest power of e is the second one, e^2. We write the gcf as 3de^2.

Indeed 3c^2de^2 = 3de^2 * c^2; 6cde^2 =3de^2 * 2c; 3de^2 = 3de^2 * 1. 

We can also factor the expression as  3c^2de^2 +  6cde^2 + 3de^2 = 3de^2 ( c^2 + 2c + 1).

Note that the expression in parentheses is a complete square c^2 + 2*c*1 + 1^2 = (c + 1)^2, so the complete factoring will look like 3c^2de^2 +  6cde^2 + 3de^2 = 3de^2 ( c + 1)^2.

Apr 15th, 2015

thank you

Apr 15th, 2015

You are welcome.

Apr 15th, 2015

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