Monday, November 30, 2015

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?