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Solve this algebraic expression

16a {}^(4) - 4a {}^(2) - 4a - 1


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

2 Answers

3 votes

Answer:

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,

User Muyueh
by
7.8k points
0 votes
(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)
Solve this algebraic expression 16a {}^(4) - 4a {}^(2) - 4a - 1 ​-example-1
User CmKndy
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8.6k points