Problem: Article: Equations with two variables factor differently than basic quadratics. For any equation a2-b2 where a and b do not equal 0, the equation factors to (a+b)(a-b). For example, the equation 9x2 - 4y2 = (3x + 2y)(3x - 2y). Note that, If the trinomial is in the form a2-2ab+b2, the factored form is slightly different: (a-b)2. The equation 4x2 + 8xy + 4y2 can be re-written as 4x2 + (2 2 2)xy + 4y2. We can now see that it's in the correct form, so we can say with confidence that our equation factors to (2x + 2y)2 Finally, it bears mentioning that cubics and even higher-order equations can be factored, though the factoring process quickly becomes prohibitively complicated. For instance, 8x3 - 27y3 factors to (2x - 3y)(4x2 + ((2x)(3y)) + 9y2)
Summary: If the equation is in the form a2-b2, factor it to (a+b)(a-b). If the equation is in the form a2+2ab+b2, factor it to (a+b)2. If the equation is in the form a3-b3, factor it to (a-b)(a2+ab+b2).

INPUT ARTICLE: Article: There are many websites that focus on selling or helping to identify replacement pieces for your china sets. You might use these resources to direct your research. These kind of sites often have an alphabetical list of china manufacturers in addition to pictures. Online appraisal services are rarely able to accurately gauge the exact worth of your dinnerware. The best use for these online services is to get direction for further research. Digital images can be of low quality or difficult to scrutinize closely, so you may want to visit a library or the antiques/collectibles section of your local book store. Using references at these places, you can compare your dinnerware to other pieces to assist with identification. Your local library may have a specific section devoted to arts and collectibles. This may be the best place to start your research. If your dinnerware has a specific name stamped on it, such as Limoges or Wedgwood, you'll likely be able to find books about those particular manufacturers. Sometimes a piece of dinnerware can appear as though it fits in a few different periods. But once you narrow down your choices to a likely few, you can compare your piece to others in that period. If you notice many similarities, chances are good the piece was produced in that period. In some cases, the back/marker stamp on the bottom of your dinnerware may give you the exact date of its production. This can help significantly with your research.

SUMMARY: Get your bearings with a brief Internet search. Utilize references from a library or bookstore. Establish a likely period in which your dinnerware was produced.

In one sentence, describe what the following article is about: These options, if pursued with a measure of dedication, will earn you a diploma while allowing you to do it at your own pace and without the social encumbrances associated with high school. This could be a great option that you can work on with your school's staff. If there's a particular field of work you're interested in, you might consider a work-study program. Not only would you be able to finish school, but you might end up graduating with job options. You might also look into early admission into Junior/Community College through a Gateway Program at your school. If you have enough credits, certain High Schools will allow you to transfer to a Community/Junior College. If you've decided that any kind of academic environment is wrong for you, you might want to start thinking about technical career paths. A GED (General Education Development), often referred to a high school-equivalency degree, is an exam that you can take to show employers that you have the education of someone with a high school diploma without having to go to school. A Certificate of High School Proficiency is something awarded by the California Department of Education to students who pass the California High School Proficiency exam (CHSPE). While the GED is meant for those 17 and up who've dropped out, the California program is meant for teenagers in the 10th grade or aged 16+.
Summary:
Consider online schools and home schooling. Think about work-study programs. Consider Gateway Programs, and Junior/Community Colleges. Think about what you'd like to do for a living. Get a GED (or Certificate of High School Proficiency).