Find the factors using a complete square

In summary, the conversation is about factoring the expression $(a+x)^2-9$ using the complete square method. The first step is to write the expression as a complete square, which is $(a+x)^2$. Then, by replacing 9 with $3^2$, we can factorize the expression as $(a+x-3)(a+x+3)$.
  • #1
mathlearn
331
0
Problem

First you are asked to,

write this expression as a complete square $x^2+2ax+a^2$

& ii. Using that find the factors of $x^2+2ax+a^2-9$

Workings

i $(a + x)^2$

Where do I need help

ii. Using that find the factors of $x^2+2ax+a^2-9$

Many Thanks :)
 
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  • #2
mathlearn said:
Problem

First you are asked to,

write this expression as a complete square $x^2+2ax+a^2$

& ii. Using that find the factors of $x^2+2ax+a^2-9$

Workings

i $(a + x)^2$

Where do I need help

ii. Using that find the factors of $x^2+2ax+a^2-9$

Many Thanks :)
You want to factorize $(a+x)^2-9$. But this is same as $(a+x)^2-3^2=(a+x-3)(a+x+3)$.
 
  • #3
caffeinemachine said:
You want to factorize $(a+x)^2-9$. But this is same as $(a+x)^2-3^2=(a+x-3)(a+x+3)$.

Thank you very much caffeinemachine :)
 

Related to Find the factors using a complete square

1. What is a complete square?

A complete square is a mathematical expression of the form (x + a)^2 or (x - a)^2, where a is a constant. It is called a complete square because it can be factored into the form of (x + b)(x + b) or (x - b)(x - b), where b is also a constant.

2. Why is finding factors using a complete square important?

Finding factors using a complete square is important because it is a useful method for simplifying and solving quadratic equations. It can also help in finding the roots or solutions of a given quadratic equation.

3. How do you find factors using a complete square?

To find factors using a complete square, you need to follow these steps:

  1. Write the quadratic expression in the form of (x + a)^2 or (x - a)^2.
  2. If the coefficient of x^2 is not 1, factor it out.
  3. Find the value of 'a' by taking half of the coefficient of x and squaring it.
  4. Add or subtract the value of 'a' inside the parentheses, and then add or subtract it outside the parentheses to maintain the equality of the expression.
  5. Factor the expression inside the parentheses by finding the common factor.
  6. Simplify the expression by combining like terms.

4. Can you use complete square method for any quadratic equation?

Yes, the complete square method can be used for any quadratic equation. However, it is most useful when the leading coefficient of x^2 is 1. If the leading coefficient is not 1, additional steps may be required to simplify the expression.

5. What are the benefits of using complete square method?

The complete square method has several benefits, including:

  • It can help in solving and simplifying quadratic equations.
  • It can help in finding the roots or solutions of a given quadratic equation.
  • It is a useful tool for graphing quadratic functions.
  • It can help in finding the minimum or maximum value of a quadratic function.

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