Hello how would I factor
81x2 −9 y2 ?
the x and y are squared

Question

Hello how would I factor
81x2 −9 y2 ? 
the x and y are squared

anonymous · Answer

what u need help on

uri · Answer

81x2 −9 y2
9xy(9x-y)

anonymous · Answer

9xy(9x-y)

anonymous · Answer

well$$81x^{2} -9y^{2}  i need help with factoring 50 cent$$

anonymous · Answer

well how did you guys get that answer

anonymous · Answer

They factored it.

uri · Answer

Take the common.

anonymous · Answer

first they divided by nine

uri · Answer

9xy was the common

anonymous · Answer

for me to understand i need you to write it out for me please or take it step by step with me because i still do not understand

zepdrix · Answer

9xy....?

$$\large 9xy(9x-y) \qquad=\qquad 81x^2y-9xy^2$$

That doesn't look like the equation he started with :\ hmm

zepdrix · Answer

$$\large 81x^2-9y^2$$81 = 9*9, so let's rewrite it that way,
$$\large 9\cdot9x^2-9y^2$$

It appears they only thing these terms have in common is a 9.
Divide a 9 out of each term,$$\large 9x^2-y^2$$Then we have to multiply each term by 9 to keep it balanced,$$\large 9(9x^2-y^2)$$

Do you understand how factoring works Sunlight?

anonymous · Answer

Hello Zepdrix I factored both 81 AND 9

zepdrix · Answer

Oh I made a boo boo... we have the `difference of squares`.. so we can simplify this down a bit further.

anonymous · Answer

and i got 9*9 xx - 3*3yy

zepdrix · Answer

Ah yes very good :) So you can rewrite each term as a square.$$\large (9x)^2-(3y)^2$$

zepdrix · Answer

And from here, we can apply a special rule.

zepdrix · Answer

$$\large a^2-b^2=(a-b)(a+b)$$

anonymous · Answer

what is the a and the b suppose to stand for?

zepdrix · Answer

I used different letters to show you a rule.
We can apply that rule to our problem.

So in our case, our a=9x, b=3y and we can break it down using the rule I posted above.

zepdrix · Answer

$$\large \color{royalblue}{a}^2-\color{red}{b}^2=(a-b)(a+b)$$$$\large \color{royalblue}{(9x)}^2-\color{red}{(3y)}^2=?$$

anonymous · Answer

(9x-3y)(9x+3y)

anonymous · Answer

is that okay?

zepdrix · Answer

Yay good job \c:/

zepdrix · Answer

Subtracting squared terms, try to remember that rule.
It comes up a lot as you advance in math classes.

anonymous · Answer

lol uhm okay but can i use the foiling method afterwards to work backwards?

zepdrix · Answer

Yes, that's a great way to check your work.

anonymous · Answer

Hey I just did the foil and I got it yay thank you thank you :o))

zepdrix · Answer

cool c:

anonymous · Answer

well okay good bye for now