Find the factors using a complete square

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SUMMARY

The discussion focuses on rewriting the expression $x^2 + 2ax + a^2$ as a complete square, resulting in $(a + x)^2$. Subsequently, it addresses the factorization of the expression $x^2 + 2ax + a^2 - 9$, which simplifies to $(a + x)^2 - 3^2$. The final factors are determined to be $(a + x - 3)(a + x + 3). This method utilizes the difference of squares to achieve the factorization.

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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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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 $(a+x)^2-3^2=(a+x-3)(a+x+3)$.
 
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 :)
 

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