Factorise x² + 2x + 1 - y²

After trying this for ages, I looked at the answer and its

(x + 1 - y)(x + 1 + y)

but I still can't get to that point by myself, can anyone help please

Thanks

- Oct 6th 2009, 11:52 PMOllieRowntreeJust started doing maths again last week, stuck on factorising problem
Factorise x² + 2x + 1 - y²

After trying this for ages, I looked at the answer and its

(x + 1 - y)(x + 1 + y)

but I still can't get to that point by myself, can anyone help please

Thanks - Oct 7th 2009, 12:13 AMGrandad
Hello OllieRowntree

Welcome to Math Help Forum!Two facts that you need to learn:

- $\displaystyle x^2+2x+1 = (x+1)^2$

- $\displaystyle a^2-b^2 = (a+b)(a-b)$

If you know these, you can use them very easily to solve your problem:

$\displaystyle x^2+2x+1-y^2 = (x+1)^2-y^2$

Can you now apply the second of the two facts to finish the job?

Grandad