Solve this algebraic expression 16a {}^(4) - 4a {}^(2) - 4a - 1 ​

Question

Solve this algebraic expression

`16a {}^(4) - 4a {}^(2) - 4a - 1`
​

Answer 1

The factored form is,

`(4a^2+2a+1)(4a^2-2a-1)`

Explanation:

We have,

`16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\`

Using the difference of square formula,

`x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)`

Which is the factored form,

Answer 2

(40'+ 227) (46 -301)
SOLVING STEPS
Tat-42-40-1
= baT.
(40'740#1)
=16a4 - pati)? = (a'+ zaHi) (42°- 20-1) a'+ sabtb"= atbs
a-B'= (ath) (0-1)