Question

Check my answer!
Determine if the expression is a perfect square and if it is, factor it.
16a^2 + 8a + 1

A. (a – 4)(a – 4)
B. not a perfect square
C. (4a + 1)2
D. (a + 4)(a – 4)
My answer: B. You can read and check my reasoning below.

Answer 1

\[16a^2 = 4a.~16a^2~is~a~perfect~\square.\]\[1=1^2. ~One~is~a~perfect~\square.\]

Answer 2

b or d i think it is

Answer 3

I believe 8a is supposed to be twice the product of the square roots of the first and last terms (AKA 16a^2 and 1).

Answer 4

Oh, um, unless you have an explanation, please do not give out a direct answer. Thank you. @officialkeily

Answer 5

sorry

Answer 6

It's okay. :) Just remember to read the Code-of-Conduct for the rules. http://openstudy.com/code-of-conduct

Answer 7

ok

Answer 8

Back to the problem, the expression would then be: \[8a = 2(4a \times 1)\]\[8a = (2 \times 4a)(2 \times 1)\]\[8a = 8a \times 2\]\[8a \neq 16a\]I guess that makes this expression not be a perfect square.

Answer 9

@asnaseer This is my work so far. Is my progress correct?

Answer 10

I am pretty sure you are wrong :)

Answer 11

:O :(

Answer 12

Factoring 16a2+8a+1

The first term is, 16a2 its coefficient is 16 .
The middle term is, +8a its coefficient is 8 .
The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 16 • 1 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 8 .

-16 + -1 = -17
-8 + -2 = -10
-4 + -4 = -8
-2 + -8 = -10
-1 + -16 = -17
1 + 16 = 17
2 + 8 = 10
4 + 4 = 8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 4
16a2 + 4a + 4a + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
4a • (4a+1)
Add up the last 2 terms, pulling out common factors :
1 • (4a+1)
Step-5 : Add up the four terms of step 4 :
(4a+1) • (4a+1)
Which is the desired factorization

Answer 13

Does that help at all?

Answer 14

@BlossomCake ?

Answer 15

Yes, it does help. But between steps 3 and 4, where does 16 go?

Answer 16

We no longer need it as you can see.

Answer 17

Keep in mind step 3 does say we are rewriting the expression :).

Answer 18

Oh, yeah. Sorry. So which answer is correct then, D.?

Answer 19

WAIT! Nevermind, the answer is C. Sorry that I am so slow. :')

Answer 20

Thank you for all your help and explaining.

Answer 21

*all of your

Answer 22

Sure thing.!

Answer 23

:D