1. ## binomial

I need to factor this completely:

$\displaystyle 16x^2 - (y + 3)^2$

$\displaystyle 16x^2 - (y + 3)^2 = [16x - (y+3)]^2 = [4x - (y+3)]^2 = (2x - y - 3)(2x + y + 3)$

but the answer in the packet says:

$\displaystyle (4x + y + 3)(4x - y - 3)$

My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?

2. Originally Posted by lax600
I need to factor this completely:

$\displaystyle 16x^2 - (y + 3)^2$

$\displaystyle 16x^2 - (y + 3)^2 = [16x - (y+3)]^2 = [4x - (y+3)]^2 = (2x - y - 3)(2x + y + 3)$

but the answer in the packet says:

$\displaystyle (4x + y + 3)(4x - y - 3)$

My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?
You're just not correctly converting the difference of squares. We have:

$\displaystyle 16x^2 = a^2$

$\displaystyle (y+3)^2 = b^2$

Hence, $\displaystyle a = 4x$ and $\displaystyle b = y + 3$.

So, using the formula $\displaystyle a^2 - b^2 = (a + b)(a - b)$ we have:

$\displaystyle (4x + y + 3)(4x - y - 3)$.

3. Oh! Alright thanks ^^