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## Proving Polynomial Identities

#### High School - HSA-APR.C.4

How to Prove Polynomial Identities When you deal with algebra, you deal with various polynomial identities that make simplification a lot easier. In other words, these identities are formulae which are proved by mathematicians. However, we can prove it also and create new formulae as well. Let us consider an example, where (x2 + y2)2 = (x2 - y2)2 + (2xy)2 is an identity Let us take Left-hand-side first (x2 + y2)2 Let us expand by using the multiplicative and distributive property (1) x4 + 2x2y2 +y4 We will leave it here. Let us take Right-hand-side first: (x2 - y2)2 + (2xy)2. Let us expand by using the multiplicative and distributive property (2) x4 - 2x2y2 +y4 + (4x2y2) - Now let us put both sides together: x4 + 2x2y2 +y4 = x4 - 2x2y2 +y4 + (4x2y2). x4 + 2x2y2 +y4 = x4 + 2x2y2 +y4 Here, we can conclude that both identities are the same. A series of worksheets and lessons that help students learn the necessary step to proving that polynomial identities are true.

### Printable Worksheets And Lessons  #### Homework Sheets

Finding the square is what it is all about.

• Homework 1 - Find the square and write your answer in the simplest form.
• Homework 3 - This can usually be done in three steps.

#### Practice Worksheets

I find that students have trouble with the square of fractions within operations.

• Practice 1 - When you look under the hood, polynomial identities are really just polynomials that are true.
• Practice 2 - We approach this one from all different levels.
• Practice 3 - Find the end value of these polynomials.

#### Math Skill Quizzes

The difficulty level here is very mixed.

• Quiz 1 - We involve simple square roots.
• Quiz 2 - The value just get larger.
• Quiz 3 - A few more fractions in here.