Answer:
This polynomial can be simplified to a difference of squares
[tex]16a^2 - 4a + 4a - 1=(4a-1)(4a+1)[/tex]
Step-by-step explanation:
Simplify the expression
[tex]16a^2 - 4a + 4a - 1\\\\16a^2- 1[/tex]
remember that 4 ^ 2 = 16
Therefore
[tex]16a^2- 1= 4^2a^2 -1[/tex]
Remember that
[tex](4a) ^ 2 = 4 ^ 2a ^ 2[/tex]
[tex]4^2a^2 -1=(4a)^2 -1[/tex]
As [tex]1 ^ 2 = 1[/tex] then
[tex](4a)^2 -1= (4a)^2 -1^2[/tex]
Remember that [tex]c ^ 2 -b ^ 2 = (c + b) (c-b)[/tex]
In this case [tex]c = 4a[/tex] and [tex]b = 1[/tex]
Finally
[tex](4a)^2 -1^2 = (4a-1)(4a+1)[/tex]
