Hey! Do you think you could create some example problems for me and walk me through it so I learn how to solve questions like this?

Question

anonymous · Answer

Factor completely 4x2 - 81 

Here is the question could you make something like it so i can learn how to solve it?

anonymous · Answer

raised to the second power

amistre64 · Answer

interactmath.com

tons of practice problems, free

enter, pick a textbook on your subject, and practice to your hearts content

nnesha · Answer

$$\huge\rm 9x^2 - 64 $$

amistre64 · Answer

if your just looking for a difference of squares .. 

a^2 x^2 - b^2 = (ax+b)(ax-b)

its a formula that needs no real practice.

anonymous · Answer

So from this equation 4x2 - 81 what would go into the "ax" part of the formula?

amistre64 · Answer

sqrt(4x^2)

anonymous · Answer

So would you just divide everything by two?

amistre64 · Answer

no, youd just take the sqrt of the first term ... as indicated

anonymous · Answer

Because wouldnt it be (2x + 9)

anonymous · Answer

So take the square root of each number?

amistre64 · Answer

yes;  (2x+9) (2x-9)

anonymous · Answer

So my next question is how do you know if you need the addition sign or the minus sign?

amistre64 · Answer

in which part are you refering?

a^2x^2 - b^2  or the factorization? (ax+b)(ax-b)

anonymous · Answer

the factorization.. Like why is it (2x+9) (2x-9) rather than two addition signs or two minus signs?

amistre64 · Answer

foil it out ...

anonymous · Answer

How would you do that? Because the equation 4x^2 - 81 only has a minus sign?

amistre64 · Answer

foil ... it .... they teach you how to multiply binomials before they want you to factor them right?

amistre64 · Answer

the best way to see it is to actually work the process ... multiply (2x+9) and (2x-9)

see what happens along the way

anonymous · Answer

They did i under stand there is such thing as the foil method like first outer inner and last but i dont really remember how to do it..

amistre64 · Answer

great, memorization of a memory trick is only as good as memorizing sooo many tricks ...

then just use distribution

amistre64 · Answer

(2x + 9) (2x - 9)  distribute it

2x(2x - 9) + 9(2x - 9)  and distrbute again  

4x^2 - 18x + 18x - 81

what happens to the middle terms?

anonymous · Answer

Youd combine them so 36x^2?

amistre64 · Answer

look at it again ... or better yet, you work it out instead of trying to follow it along ... there is something real obvious you are glancing over in this.

anonymous · Answer

would you just take it out?

anonymous · Answer

Im not really sure to be honest

amistre64 · Answer

why take it out?  

-18x + 18x

what happens to them?

anonymous · Answer

Wouldnt they cancel out because its a negative 18.. then you would add 18 back to it? so would it just be x^2?

amistre64 · Answer

$$(2x+9)(2x-9)=4x^2 - 18x + 18x - 81$$
$$4x^2 \underbrace{\color{red}{- 18x + 18x}}_{=0} - 81\implies 4x^2-81$$

amistre64 · Answer

does this only happen in this single case?  or for all cases?

anonymous · Answer

Ohh so they "x" would also cancel out?

amistre64 · Answer

yep:  -18(4) + 18(4) = 0  just as it would for any other value of x

anonymous · Answer

It would always equal 0 if its a negative number with a positive number

anonymous · Answer

But if they were both positive you would just add them together, correct?

amistre64 · Answer

the simple consequence of doing:
$$(ax+b)(ax-b)\implies a^2x^2-b^2$$
its just becasue that is the way the math works out.

if they are both positive, they have a different consequence of the distribution
$$(ax+b)^2=(ax+b)(ax+b)\implies a^2x^2+b^2+2abx$$

amistre64 · Answer

if they are both negative, the consequence is a -2abx  on the end instead ....

anonymous · Answer

Ohh okay I gotcha :)

anonymous · Answer

Thank you Sir

amistre64 · Answer

your welcome

nnesha · Answer

$\color{blue}{\text{Originally Posted by}}$ @yoyogators
the factorization.. Like why is it (2x+9) (2x-9) rather than two addition signs or two minus signs?
$\color{blue}{\text{End of Quote}}$
if there is a negative sign in original question 
then answer always going to be (  # + #  ) (#.. - ..#.) one plus and one minus sign  
 :-)

nnesha · Answer

4x^2 + 9 
can you factor this one ??

anonymous · Answer

Would they both be positive?

nnesha · Answer

for that  one you can't USE  *DIFFERENCE OF SQUARE METHOD*
 :-)

anonymous · Answer

So would it be similar to what he said above. Would it be like this? "a2x2+b2+2abx"

nnesha · Answer

that equation is not  factorable  :-)

nnesha · Answer

in order to use difference square method there should be negative sign 
and both therms should be perfect square root :-) |dw:1430011994606:dw|