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
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.)
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?