Factorization of a polynomial: HELP!!

[elephantsize]

Can anyone help me with factorizing this polynomial???
4a2 - 4b2 + 4a +1, i.e.
4(a squared) - 4(b squared) + 4a +1
over

 

[tkhunny]

Can anyone help me with factorizing this polynomial???
4a2 - 4b2 + 4a +1, i.e.
4(a squared) - 4(b squared) + 4a +1
over

I'd be tempted to write it like this, first: (4a^2 + 4a +1) - (4b^2)

Now what?

 

[TchrQbic]

Can anyone help me with factorizing this polynomial???
4a2 - 4b2 + 4a +1, i.e.
4(a squared) - 4(b squared) + 4a +1
over

Your first step should be to consider regrouping terms in this polynomial. You can try grouping 4a^2 and 4a and removing any common factor. Or you might group (4a^2 + 4a) - (4b^2 - 1)

Those two groups are differences of squares that can be factored by the pattern: (x^2 - y^2) = (x+y)(x-y)

Try that and see how far you can get.

 

[stapel]

Your first step should be to consider regrouping terms in this polynomial. You can try grouping 4a^2 and 4a and removing any common factor. Or you might group (4a^2 + 4a) - (4b^2 - 1)....

I agree with the regrouping idea. But in order to factor the polynomial (rather than just some of its terms), I think one would do much better to use the grouping suggested by tkhunny. This will create a true difference of squares, enabling the polynomial -- as a whole -- to be factored.

Eliz.