Question

9^2 + (c-1)^2

My book says its 81 + C^2 - 2c +1

How is that correct?

Why wouldnt it just be

81^2 + C^2 +1 ??

It makes no sense to me?

(c-2)^2 i thought was just C^2 +1

Please help

Answer 1

Crap the bottom part i typed wrong i thought (c-1)^2 was C^2 +1

Answer 2

(a-b)^2 = a^2 - 2*a*b - b^2

Answer 3

When multiplying binomials use FOIL (First, Outside, Inside, Last)

so for (c-1)^2 this is the same as (c-1)*(c-1)
multiply the First terms of each binomial so c*c=c^2
multiply the Outside terms of each binomial so c*(-1)=-c
multiply the Inside terms of each binomial so c*(-1)=-c
multiply the Last terms of each binomial so (-1)*(-1)=1
Then add them all together to get:
c^2+(-c)+(-c)+1 which simplifies to:
c^2-2c+1

so 9^2 + (c-1)^2=81+c^2-2c+1

Answer 4

How is that possible if (c-1)^2 is the same as c-1 * C-1
And the powers to powers rule says we multiply the eponets although there is no eponet so its assumed its 1

Answer 5

ok so that is technically a binomial i understand that and foil.
So your saying when you have multiple terms in pareth raised to a power you can not use the powers to powers rule and just multiple the exponets

Answer 6

put in numbers and try it out:

say c=3
(3-1)^2=2^2=4
if (c-1)^2=c^2+1 it would be 3^2+1=10, this is not correct
however, with foil it is c^2-2c+1=3^2-2(3)+1=9-6+1=4, correct

Answer 7

yep, you can only use the powers to powers rule with a single number, for a binomial you have to use FOIL

Answer 8

Thank you!