How do you simplify (3c \cdot 2c ^ { 2} ) ^ { 2}?

Jun 2, 2017

${\left(3 c \cdot 2 {c}^{2}\right)}^{2}$
$= 9 {c}^{2} + 12 {c}^{3} + 4 {c}^{6}$

Explanation:

Using the formula for a perfect square
${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$
Hence:
${\left(3 c \cdot 2 {c}^{2}\right)}^{2}$
$= {\left(3 c\right)}^{2} + 2 \left(3 c\right) \left(2 {c}^{2}\right) + {\left(2 {c}^{2}\right)}^{2}$ (Use the formula)
$= {3}^{2} {c}^{2} + 2 \cdot 3 \cdot 2 \cdot c \cdot {c}^{2} + {2}^{2} {\left({c}^{2}\right)}^{2}$ (expand the brackets)
$= 9 {c}^{2} + 12 {c}^{2 + 1} + 4 {c}^{2 \cdot 2}$ (Use laws of exponents ${x}^{a} \cdot {x}^{b} = {x}^{a + b}$ and ${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$
$= 9 {c}^{2} + 12 {c}^{3} + 4 {c}^{6}$

Hope this helps!

Jun 2, 2017

$36 {c}^{6}$

Explanation:

$\text{using the "color(blue)"laws of exponents}$

color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n);(a^mb^n)^p=a^(mp)b^(np))color(white)(2/2)|)))

$\text{simplifying 'inside' the bracket}$

$3 c \times 2 {c}^{2} = 6 {c}^{3}$

$\Rightarrow {\left(6 {c}^{3}\right)}^{2}$

$= {6}^{\left(1 \times 2\right)} \times {c}^{\left(3 \times 2\right)}$

$= {6}^{2} \times {c}^{6}$

$= 36 {c}^{6}$