How do I Factor this

2(a+b)^2+5)(a+b)+3

Question

How do I Factor this

2(a+b)^2+5)(a+b)+3

waheguru · Answer

$$2(a+b)^2+5)(a+b)+3 factor$$

Can someone please explain how to factor this?

mertsj · Answer

Replace (a+b) with x and try that

waheguru · Answer

$$2(a+b)^2+5(a+b)+3  $$

mertsj · Answer

$$2x^2+5x+3$$

anonymous · Answer

Yeah. so let (a+b) = x, 

Then 2x^2+5x+3

waheguru · Answer

Why do I replace with ?

mertsj · Answer

So its easier to factor.

mertsj · Answer

More familiar looking

anonymous · Answer

u replace it with X to make the expression easier.

Later u can use this x = a+b to find proper value

waheguru · Answer

Can you also explqin how to solve without replacing it with x

mertsj · Answer

$$2x^2+5x+3=(2x+3)(x+1)$$

mertsj · Answer

$$(2x+3)(x+1)=[(2(a+b)+3][(a+b)+1]=$$

mertsj · Answer

$$(2a+2b+3)(a+b+1)$$

anonymous · Answer

well uh without replacing with x it becomes very tedious. 

thats why we do it using x = a +b

waheguru · Answer

the answer is somthine else that what I am getting? http://www.wolframalpha.com/input/?i=2%28a%2Bb%29%5E2%2B5%28a%2Bb%29%2B3+factor

anonymous · Answer

no LOL its the same :)

waheguru · Answer

I do not get how its the same?

mertsj · Answer

Yep.  
Thanks to Wolf for proving me right.

mertsj · Answer

(2a+2b+3)(a+b+1) is the same as (a+b+1)(2a+2b+3)

mertsj · Answer

4 x 3 = 3 x 4

anonymous · Answer

he means; 3 x 2 = 6 and even 2 x 3 = 6.

This is called as commutative property of multiplication.

a  x  b = b x a.

waheguru · Answer

(2x+3)(x+1) 

what did u do after I do not understand

mertsj · Answer

Replaced x with a+b

mertsj · Answer

Remember:  At the  beginning we said we would replace a+b with x so it would be easier to factor

waheguru · Answer

yea..

mertsj · Answer

Then we factored it with x and said , oh wait...x is really a+b

mertsj · Answer

I will leave now.  I think part of your confusion is that there is one too many cooks and it is confusing you.

waheguru · Answer

$$2x2+5x+3=(2x+3)(x+1)$$

Should it have been 

(2x+5)(x+3)

waheguru · Answer

@Mertsj ?

agent0smith · Answer

No, the first one was correct.

mertsj · Answer

Is 5 x 3 = 3???

waheguru · Answer

becuse we factor out x 

x(2x+5)+3
and becomes (2x+5)(x+3)

mertsj · Answer

Ok.  You can say those are the factors and I will say that the factors of 3 are 5 x3.  When and if you prove me wrong, I will prove you wrong.

waheguru · Answer

I am not contradicting what you said nor trying to prove you wrong in any way. I just don't understand how you have factored it because I am getting a different answer. I want to learn and that's why questioned you...

mertsj · Answer

That was not the point.  i was hoping you would say "The factors of 3 are not 3x 5 because 3 x 5 = 15 and not 3".

mertsj · Answer

I was trying to get you to see that whatever you say the factors are must multiply back to the original thing you factored.  And the factors of 2x^2+5x+3 could NOT be (2x+5)(x+3) because:
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