Process of factoring. A little complicated!

[predentlove]

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factor 4a^2 - 4ab - 3b^2

I do not know where to start with this one....

Hmmmm... Is there an acutal process to this? Or is this just guess and check? Usually I would use grouping.. but it doesn't seem to work here?

The solution is (2a - 3b) (2a+b)

Same method..

3a^2 - 5ab - 12b^2

Solution: (3a + 4b) (a - 3b)

Thanks x10000 for your help... What would I do without you guys?! 😍

 

[radmazindds]

I would guess and check like I would when factoring a quadratic equation.

factor 4a^2 - 4ab - 3b^2

I do not know where to start with this one....

Hmmmm... Is there an acutal process to this? Or is this just guess and check? Usually I would use grouping.. but it doesn't seem to work here?

The solution is (2a - 3b) (2a+b)

Same method..

3a^2 - 5ab - 12b^2

Solution: (3a + 4b) (a - 3b)

Thanks x10000 for your help... What would I do without you guys?! 😍

 

[predentlove]

I figured it out!!! Ugh i was just making a silly mistake.

Basically for
4a^2 - 4ab - 3b^2
4a^2 + ( )ab + ( )ab -3b^2
4a^2 + (2 )ab + (-6 )ab -3b^2
2a (2a + b) -3b ( 2a + b)
(2a - 3b) (2a +b)

the blanks must add to -4, and multiply to -12! what numbers? -6 & +2

 

[radmazindds]

nice! that's a good way of looking at it. that's essentially how factoring works with guess and check, isn't it?

i miss junior high /high school math 🙁

I figured it out!!! Ugh i was just making a silly mistake.

Basically for
4a^2 - 4ab - 3b^2
4a^2 + ( )ab + ( )ab -3b^2
4a^2 + (2 )ab + (-6 )ab -3b^2
2a (2a + b) -3b ( 2a + b)
(2a - 3b) (2a +b)

the blanks must add to -4, and multiply to -12! what numbers? -6 & +2

 

[fujindesu]

On the real DAt, it might be faster if you just trial and error, expand all the answers out til you find the solution. If it's numerical values then just plug em in and check.