Evaluate: (6a^2)/(a^2+8a+16) * (a^2-16)/(6a)

Expression: $\frac{ 6{a}^{2} }{ {a}^{2}+8a+16 } \times \frac{ {a}^{2}-16 }{ 6a }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\frac{ 6{a}^{2} }{ {a}^{2}+8a+16 } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ 6a }$

Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression

$\frac{ 6{a}^{2} }{ {\left( a+4 \right)}^{2} } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ 6a }$

Cancel out the greatest common factor $6$

$\frac{ {a}^{2} }{ {\left( a+4 \right)}^{2} } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ a }$

Cancel out the common factor $a$

$\frac{ a }{ {\left( a+4 \right)}^{2} } \times \left( a-4 \right) \times \left( a+4 \right)$

Cancel out the common factor $a+4$

$\frac{ a }{ a+4 } \times \left( a-4 \right)$

Calculate the product

$\frac{ {a}^{2}-4a }{ a+4 }$