Day: April 13, 2017

Week 9 – Three Important Polynomials Products

by nighinar2016

The distribution of the following polynomials

(a+b)^2 = (a+b)(a+b)

= a^2 + ab + ba + b^2

= a^2 +2ab + b^2

 

(a - b)^2 = (a – b)(a – b)

= a^2 – ab – ba + b^2

= a^2 – 2ab + b^2

 

(a – b)(a + b)

= a^2 + ab – ba – $latex b^24

= a^2 – b^2

When expanding and simplifying a polynomial, we can use the patterns or answers of the following polynomials to help us simplify quicker and easier.

So, when seeing the follow polynomials that fit the equation, you can go straight to the answer without having to go through all the distributive property.

This helps when simplifying longer polynomial expressions.

For example

Expand and simplify (x + 5)(x – 5) – (x + 2)(x+8)

We can go straight from (x + 5)(x – 5)  to  x^2 – 25 because we know that the terms are the same and we know the simplified answer without going through the long distribution.

Now we can continue to simplify the rest. You can’t use any of the three products from above here because (x + 2)(x+8) do not share all the same numbers.

= x^2 – 25 – (x^2 + 8x + 2x + 16)

= x^2 – 25 – (x^2 + 10x + 16)

Bring in the negative.

= x^2 – 25 – x^2 – 10x – 16

The x^2 cancels out because there is a negative and a positive one of the same thing. Continue simplifying and adding like terms.

= -10x – 41

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I found this lesson very useful. It was easy to remember once I got the hang of it and it helped me simplify polynomials quicker.