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}= a^{2}+ 2ab +b^{2}**The square of the difference in two numbers**:

(a-b)

^{2}= a^{2 }– 2ab + b^{2}**The product of the sum of two numbers and the difference in the same two numbers**

(a+b)(a-b) = a

^{2}– b^{2}
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.)

81x

^{2}-16z^{4}
169x

^{2}+ 25y^{2}- 80xy
144x

^{2 }+ 49y^{2}+ 84
One last problem:

Consider the expression

1200 x

^{2}– 3000 y^{2}
Can you rewrite this expression as the product of the
difference of terms and the sum of terms?

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