How would one factor this by hand

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In summary, the conversation discusses a method for solving a quadratic equation by hand without assuming knowledge of the perfect square formula. The website provided on the topic suggests using the method of completing the square, and a specific example is given. The conversation also mentions the use of expanding (a+b)^2 to arrive at the perfect square formula.
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[SOLVED] How would one factor this.. by hand..

Assuming I didn't know the perfect square formula ( (a+-b)^2), how would I go about solving this equation by hand factoring?

x^2 + b/a *x + b^2 / 4a^2 = 0

I am trying to figure out how the quadratic formula is derived, and this is one part of deriving the equation in which I am unable to hand factor(assuming I didn't know perfect squares formula), how would one go about doing this ?

It is included on a website(step 3 and 4), http://www.1728.com/quadr2.gif"

Can someone show me the steps to factoring that by hand?
 
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  • #2
how about (x+b/(2a))^2
 
  • #3
Do you what "completing the square" is?

Wait, are you asking for a method to do with without assuming you know [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]? If you don't want to assume it, just show it first. Expand.

[tex](a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2[/tex].
 
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Related to How would one factor this by hand

1. How do I identify common factors when factoring by hand?

To identify common factors when factoring by hand, you must first look for any numbers or variables that are shared between all of the terms in the expression. These common factors can then be factored out of each term to simplify the expression.

2. What is the process for factoring by hand?

The process for factoring by hand involves identifying common factors, using the distributive property to simplify the expression, and then using various factoring techniques such as the difference of squares or grouping to factor the remaining terms.

3. How do I know when an expression is fully factored?

An expression is fully factored when there are no common factors left to be factored out and all remaining terms are in their simplest form. You can also check by multiplying the factored terms together to see if they equal the original expression.

4. Can all expressions be factored by hand?

No, not all expressions can be factored by hand. Some expressions, such as prime numbers or expressions with irrational numbers, cannot be factored further. In these cases, the expression is considered to be in its simplest form.

5. Are there any shortcuts or tricks for factoring by hand?

Yes, there are some common shortcuts and tricks for factoring by hand. These include looking for common patterns, using the difference of squares formula, and using the quadratic formula for expressions with a quadratic term. However, these shortcuts may not work for every expression and it is important to understand the underlying concepts of factoring.

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