How would I factor the following equations?

a) 49-(2y-w)^2
b) x^2+6xy+9y^2-36

Question

How would I factor the following equations?

a) 49-(2y-w)^2
b) x^2+6xy+9y^2-36

anonymous · Answer

I tried (7-2y-w)(7+2y-w) for the first one, but I don't think it gives the same answer when expanded out.

anonymous · Answer

that is almost right but you may have forgotten some parentheses and the distributive law

anonymous · Answer

not $$(7-2y-w)(7+2y-w) $$ but rather $$(7-(2y-w))(7+(2y-w)) $$

anonymous · Answer

That makes sense, but I was wondering how I'd expand the factored form (the reverse)?

anonymous · Answer

your job is to factor, not expand
you can rewrite this as 
$$(7-2y+w)(7+2y-w)$$ if you like

anonymous · Answer

if you expand it you get what you started with 
$$a^2-b^2=(a-b)(a+b)$$

anonymous · Answer

Oh, okay. Thank you! Do you by any chance know how the second one is factored?

jim_thompson5910 · Answer

hint:

x^2+6xy+9y^2

factors to

(x+3y)^2

anonymous · Answer

Ohh, okay I got it. Thank you! It just confused me because of the number of terms.

jim_thompson5910 · Answer

that's great it's making sense now, yw

jim_thompson5910 · Answer

what do you get for the final answer

anonymous · Answer

I was trying to group the terms before.

anonymous · Answer

It would be (x+3-6)(x+3+6), right?

jim_thompson5910 · Answer

it should be (x+3y-6)(x+3y+6)

but you just forgot about the y's

anonymous · Answer

oops, yeah. Just realized. Thanks again

jim_thompson5910 · Answer

yw