Question

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

Answer 1

`(3c*2c^2)^2`
`=9c^2+12c^3+4c^6`

Explanation:

Using the formula for a perfect square
`(a+b)^2=a^2+2ab+b^2`
Hence:
`(3c*2c^2)^2`
`=(3c)^2+2(3c)(2c^2)+(2c^2)^2` (Use the formula)
`=3^2c^2+2*3*2*c*c^2+2^2(c^2)^2` (expand the brackets)
`=9c^2+12c^(2+1)+4c^(2*2)` (Use laws of exponents `x^a*x^b=x^(a+b)` and `(x^a)^b=x^(a*b)`
`=9c^2+12c^3+4c^6`

Hope this helps!

Answer 2

`36c^6`

Explanation:

`"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)|)))`

`"simplifying 'inside' the bracket"`

`3cxx2c^2=6c^3`

`rArr(6c^3)^2`

`=6^((1xx2))xxc^((3xx2))`

`=6^2xxc^6`

`=36c^6`