Questions regarding my next phase in self taught algebra

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July 9th 2009, 09:50 AM
allyourbass2212

Questions regarding my next phase in self taught algebra

Hello everyone, I have almost completed the self teaching guide through Algebra I. The last chapters end with quadratic polynomial expressions, equations, and applications e.g. in the form $ax^2+bx+c$

While I was surfing through some posts today I stumbled across this expression. Im not sure what to call $(8a^3+1)$ because it is not a quadratic expression yet it is factored in a seemingly similar manner.

$<br /> (8a^3+1)=(1+2a)(1-2a+4a^2)$

Would some one please tell me what this type of expression is and what the rules for factoring it are?

Also when might I expect to see expressions beyond quadratic polynomials? Algebra II?

Thank you
July 9th 2009, 09:55 AM
e^(i*pi)

Quote:

Originally Posted by allyourbass2212

Hello everyone, I have almost completed the self teaching guide through Algebra I. The last chapters end with quadratic polynomial expressions, equations, and applications e.g. in the form $ax^2+bx+c$

While I was surfing through some posts today I stumbled across this expression. Im not sure what to call $(8a^3+1)$ because it is not a quadratic expression yet it is factored in a seemingly similar manner.

$<br /> (8a^3+1)=(1+2a)(1-2a+4a^2)$

Would some one please tell me what this type of expression is and what the rules for factoring it are?

Also when might I expect to see expressions beyond quadratic polynomials? Algebra II?

Thank you

The formula they're using to factor this is the sum/difference of two cubes - a special case when factoring cubics:

$a^3 \pm b^3 = (a+b)(a^2 \mp ab + b^2)$

In your case a = (2a) and b=1
July 9th 2009, 10:01 AM
Kasper

This type of question trips people up because $(8a^3+1)$ doesnt seem to belong to the factoring equation $x^3+y^3=(x+y)(x^2-xy+y^2)$ when it actually does.

Note that $(8a^3+1)=((2a)^3+1^3)$

Now just apply that to $x^3+y^3=(x+y)(x^2-xy+y^2)$ .