Monday, November 30, 2015

Three Common Quadratic Equations

Three Common Quadratic Equations

This post may help some people studying for an algebra exam.


Many types of quadratic equation problems involve three common situations.


The square of a sum of two numbers:


(a+b)2 = a2 + 2ab +b2


The square of the difference in two numbers:

(a-b)2 =  a2 – 2ab  + b2



The product of the sum of two numbers and the difference in the same two numbers


(a+b)(a-b)   = a2 – b2


The three common quadratic equations can be used to recognize patterns and simplify more complex problems.

Simplify the following expressions:  (Hint:  a=4x and b=7y)


(4x + 7y)2


(4x-7y)2


(4x+7y) (4x-7y)



Recognition of the three common quadratic equations can also be use to factor a complex polynomial.

Factor the following polynomials:  (Hint:  Each of the expressions below corresponds to one of the four quadratic types.    You need to identify the expressions that belong to a, b and when appropriate 2ab.)



81x2   -16z4


169x2 +   25y2    - 80xy


144x2 +  49y2  + 84



One last problem: 

Consider the expression 


1200 x2 – 3000 y2



Can you rewrite this expression as the product of the difference of terms and the sum of terms?

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