Factor the expression into a product of binomials.
25a^2-70ab+49b^2
Is this the same as before??

Question

anonymous · Answer

I have 4 different choices

anonymous · Answer

yes!

anonymous · Answer

is it going to be (25a+49b)(25a-49b)?

2bornot2b · Answer

$$25a^2-70ab+49b^2\implies (5a-7b)^2\implies(5a-7b)(5a-7b)$$

2bornot2b · Answer

thats wrong sinz

anonymous · Answer

how do we get the 70 what = it

anonymous · Answer

$ (5 a-7 b)^2 $

anonymous · Answer

5 * 7 = 35, since you have two of these, double it to get 70

anonymous · Answer

okay that's what I was wondering is if you doubled the 35?

2bornot2b · Answer

$$25a^2-70ab+49b^2\implies25a^2-(2\times5a\times 7b)+49b^2\implies(5a-7b)^2\implies(5a-7b)(5a-7b)$$

anonymous · Answer

your equation ran off the screen just to let you know

2bornot2b · Answer

It comes from the famous formula...$$(a+b)^2=a^2+2ab+b^2$$

anonymous · Answer

^it's not a formula, just expansion ;)

2bornot2b · Answer

what exactly is the difference between the two terms?

anonymous · Answer

so does this go with the same equation then 25x^2- 60xy+36y^2

2bornot2b · Answer

Not arguing though.. I would love to know

anonymous · Answer

haha, it's okay, IMO formula is abstract term, where as expansion is much more concrete ;)

2bornot2b · Answer

@sinz yes the expression $$25x^2- 60xy+36y^2$$ can be dealt in a similar way

2bornot2b · Answer

@fool for math, can you show me an example so that I understand better.

anonymous · Answer

okay so it would be (5x - 6y)^2 right?

2bornot2b · Answer

@sinz yes you are right

anonymous · Answer

Formula is something that you will like to memorize, expansion is more like understanding what's happening pertaining to the above binomial expansion.

anonymous · Answer

SOme people memorize it as a formula and then understand the expansion

anonymous · Answer

others, understand the expansion and then try to generalize it as a formula.

anonymous · Answer

btw the binomial expansion or formula whatever you call it, it's originated from the study of the expansion and then trying to somehow form a closed a form

anonymous · Answer

you can call the closed form as formula, but unless you understand the expansion it's not worth-awhile memorizing the formula.

2bornot2b · Answer

Okay okay, got the hint. Thanks @foolformath

anonymous · Answer

This was how pascal triangles was formed .. and further research on identities like hockey sticks and depth analysis of combinatorics started .

anonymous · Answer

it's fantastic actually, now if you just memorize it as a formula you are missing a whole lot of mathematics :D

anonymous · Answer

Glad to help :)