Algebra Math Helped Needed Pretty Please (Due by Thursday March 17Th 2011 $5 BONUS ) 75

Algebra Math Helped Needed Pretty Please (Due By Thursday March 17th 2011 $5 BONUS!!!) 75 words max

1. Provide one real-world application of algebraic concepts as it would apply to business. Show your work. Did you have any difficulty with this activity? Explain why or why not.

Algebra finds extensive use in day to day and business applications. For example, if price of 1 stock is $12.50. We can find the price of 100stocks just by multiplying 12.50 by 100 that is $1250.

Suppose we have to find out the sum of $1000 deposited in a bank if bank pays 6% interest rate annually. The sum will be 1000*(1+6/100) = 1060 after 1 year. There can be similar application of Algebra. There was no difficulty with this activity as it is application of Algebra.

2. Explain how to factor the following trinomials forms: x^2 + bx + c and ax^2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Suppose we want to factorize x2+bx+c. To factorize, we make whole square of x terms. For this, we take square root of 1st term. It is x as 1st term is x2. Double the square root; it is 2x. Divide the middle term, that is, bx by 2x and (b/2). Add and subtract of b/2. We can proceed as given below.

We have x2+bx+c =

This is how we can factorize x2+bx+c.

Let us factorize ax2+bx+c. We multiply the expression by a so that 1st term becomes whole square and proceed as above.

We have Multiplying and dividing expression by a.

Square root of 1st term is ax. Divide abx by 2ax and get b/2.

Add and subtract b2/4.

Making whole square of x terms

Writing 2nd term as square.

This is how we can factorize the given expression.

There can be more than one way of factorizing but ultimate result will be same.

3. How do you factor the difference of two squares? How do you factor the perfect square trinomial? How do you factor the sum and difference of two cubes? Which of these three makes the most sense to you? Explain why.

Let us factorize a2-b2.

We have Adding and subtracting ab.

Taking common factors.

This is how we can factorize.

Let us factorize a2+2ab+b2.

We have

Let us factorize a3+b3.

We have .

Hence,

This is how we can factorize sum of two cubes.

Let us factorize a3-b3.

We have

Or,

This is how we can factorize difference of two cubes.

Factorizing difference of two squares makes most as it we can very easily factorize just by seeing difference of two squares.