Questions regarding my next phase in self taught algebra

• Jul 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 $\displaystyle ax^2+bx+c$

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

$\displaystyle (8a^3+1)=(1+2a)(1-2a+4a^2)$

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
• Jul 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 $\displaystyle ax^2+bx+c$

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

$\displaystyle (8a^3+1)=(1+2a)(1-2a+4a^2)$

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:

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

In your case a = (2a) and b=1
• Jul 9th 2009, 10:01 AM
Kasper
This type of question trips people up because $\displaystyle (8a^3+1)$ doesnt seem to belong to the factoring equation $\displaystyle x^3+y^3=(x+y)(x^2-xy+y^2)$ when it actually does.

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

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