# Polynomials/Factor

• Apr 27th 2012, 08:35 PM
Kibbygirl
Polynomials/Factor
I've gone through my notes and I can't find any to help me solve the following, could anyone help me please?

1. Multiply:
(n+6)3

Do you do n3+216?

2. Factor:
x3+125

3. Factor:
16a4-1
• Apr 27th 2012, 08:50 PM
Prove It
Re: Polynomials/Factor
Quote:

Originally Posted by Kibbygirl
I've gone through my notes and I can't find any to help me solve the following, could anyone help me please?

1. Multiply:
(n+6)3

Do you do n3+216?

2. Factor:
x3+125

3. Factor:
16a4-1

1. Absolutely not. Either write it out in full as \displaystyle \displaystyle \begin{align*} (n + 6)(n + 6)(n + 6) \end{align*} and expand, or apply \displaystyle \displaystyle \begin{align*} (a + b)^3 = a^3 + 3a^2b + 3a\,b^2 + b^3 \end{align*}.

2. Apply the sum of two cubes rule.

3. Write it as \displaystyle \displaystyle \begin{align*} \left(4a^2\right)^2 - 1^2 \end{align*} and apply the Difference of Two Squares rule.
• Apr 27th 2012, 08:51 PM
princeps
Re: Polynomials/Factor
$\displaystyle (a+b)^3=a^3+3a^2b+3ab^2+b^3$

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

$\displaystyle a^4-b^4=(a-b)(a+b)(a^2+b^2)$