## Proving Polynomial Identities

#### Aligned To Common Core Standard:

**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
(x^{2} + y^{2})^{2} Let us expand by using the multiplicative and distributive property
(1) x^{4} + 2x^{2}y^{2} +y^{4} 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) x^{4} - 2x2y^{2} +y^{4} + (4x^{2}y^{2}) - Now let us put both sides together: x^{4} + 2x^{2}y^{2} +y^{4} = x^{4} - 2x^{2}y^{2} +y4 + (4x^{2}y^{2}). x4 + 2x^{2}y^{2} +y^{4} = x^{4} + 2x^{2}y^{2} +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

- Finding the Square Step-by-step
Lesson- Work on finding the square of the binomial.

- Guided Lesson -
Find the square of the polynomial sums and differences.

- Guided Lesson Explanation
- I show you how to form polynomials using two simple calculations.

- Practice Worksheet
- Evaluate all the binomial squares and simplify them.

- Matching Worksheet
- Match the binomials to the polynomials that they create.

#### 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 2 - Start with what you know about the square of the binomial.
- 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.