# How do you multiply ((t+2)^3/(t+1)^3*(t^2+2t+1)/(t^2+4t+4)*(t+1)/(t+2)) ?

Apr 13, 2018

1

#### Explanation:

First, we start by factoring $\frac{{t}^{2} + 2 t + 1}{{t}^{2} + 4 t + 4}$

$\frac{{\left(t + 1\right)}^{2}}{{t}^{2} + 4 t + 4}$ Factoring the numerator first.

$\frac{{\left(t + 1\right)}^{2}}{{\left(t + 2\right)}^{2}}$ Then factoring the denominator.

Now, it is easy to multiply:

${\left(t + 1\right)}^{2} / {\left(t + 2\right)}^{2} \cdot \frac{t + 1}{t + 2} = {\left(t + 1\right)}^{3} / {\left(t + 2\right)}^{3}$

Finally, we can multiply

${\left(t + 1\right)}^{3} / {\left(t + 2\right)}^{3} \cdot {\left(t + 2\right)}^{3} / {\left(t + 1\right)}^{3} = \frac{{\left(t + 1\right)}^{3} \cdot {\left(t + 2\right)}^{3}}{{\left(t + 1\right)}^{3} \cdot {\left(t + 2\right)}^{3}} = \frac{1}{1} = 1$