Question

16b2c12–0.25 Factor Completey

Answer 1

`(4bc^(6) - (1)/(2))(4bc^(6) + (1)/(2))`

Explanation:

Given

`16b^2c^(12) - 0.25`

Required

Factor Completely

Follow the steps below;

Rewrite 0.25 as a fraction

`16b^2c^(12) - (25)/(100)`

Simplify fraction to lowest term

`16b^2c^(12) - (1)/(4)`

Expand
`16b^2c^(12)`

`4^2b^2c^(6*2) - (1)/(4)`

`(4bc^(6))^2 - (1)/(4)`

Expand
`(1)/(4)`

`(4bc^(6))^2 - (1)/(2)*(1)/(2)`

`(4bc^(6))^2 -( (1)/(2))^2`

From laws of product of two squares

`a^2 - b^2 = (a+b)(a-b)`

So,

`(4bc^(6))^2 -( (1)/(2))^2` is equivalent to

`(4bc^(6) - (1)/(2))(4bc^(6) + (1)/(2))`

The expression cannot be factorized any further;

Hence, the factor of
`16b^2c^(12) - 0.25` is
`(4bc^(6) - (1)/(2))(4bc^(6) + (1)/(2))`