# binomial

• May 7th 2008, 04:02 PM
lax600
binomial
I need to factor this completely:

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

$
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:

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

My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?
• May 7th 2008, 04:10 PM
icemanfan
Quote:

Originally Posted by lax600
I need to factor this completely:

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

$
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:

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

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:

$16x^2 = a^2$

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

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

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

$(4x + y + 3)(4x - y - 3)$.
• May 7th 2008, 04:17 PM
lax600
Oh! Alright thanks ^^