factor this 4c^2+4c+1

Question

I need help factoring this expression

Answer 1

Hi Hannah,

 

Start with your factor brackets: (__c + ___)(___c + ___). We know they are both '+' as the problem is all addition.

So for the spaces before the 'c' you need factors of 4 that are positive. (1, 4), (4, 1), (2, 2)

For the spaces after the '+' you need factors of 1 that are also positive. (1, 1)

 

Now we know that we have: (__c + 1)(__c + 1). Now what do we need to fill into each space to create the middle term 4c. As both will be multiplied by 1, we need the sum of the factors to equal 4, the coefficient of the middle term, 4c. 

   1 + 4 = 5 no

   4 + 1 = 5 no

   2 + 2 = 4 YES!

 

Let's give it a try! (2c + 1)(2c + 1) = ??  Distribute the terms

 

2c(2c) = 4c²  (Is this your first term? Yes!)

2c(1) = 2c

1(2c) = 2c     Add like terms: 2c + 2c = 4c. (Is this your middle term? Yes!)

1(1) = 1        (Is this your last term? Yes!)

 

Therefore, (2c + 1)(2c + 1) = 4c² + 4c + 1  (Check!)