Chapter P.5, Problem 8CVC

Here is a list of the factoring techniques that we have discussed.

a. Factoring out the GCF

b. Factoring by grouping

c. Factoring trinomials by trial and error

d. Factoring the difference of two squares

$A^2-B^2=(A+B)(A-B)$

e. Factoring perfect square trinomials

$\begin{array}{l}{A}^2+2AB+B^2={(}^A\\ A^2-2AB+B^2={(}^A\end{array}$

f. Factoring the sum of two cubes

$A^3+B^3=(A+B)(A^2-AB+B^2)$

g. Factoring the difference of two cubes

$A^3-B^3=(A-B)(A^2+AB+B^2)$

The algebraic expression ${(x+1)}^{\frac{1}{2}}-\frac{1}{3}{(x+1)}^{\frac{3}{2}}$ can be factored using______ as the greatest common factor.

Fill in each blank by writing the letter of the technique (a through g) for factoring the polynomial.