Can someone help me please
Factor completely.
81x^2-25
show all work please

Question

Can someone help me please
Factor completely.
81x^2-25
show all work please

fluttershyk · Answer

81x^2 +25= 0 

 81x^2 = - 25 

 x^2 = -25/81 

 x= + or - sqrt (-25/81) 

 sqrt (-25/81) = sqrt (25/81) x sqrt(-1) 

 = 5/9 (i) 

 so x= 5i/9 or x= -5i/9

563blackghost · Answer

We have

$\Huge{81x^{2} -25}$ 

To factor we find a number that will multiply to equal $\large{81x^{2}}$

What number would that be?

ayanaortega · Answer

i kinda of don't under stand factor, can you explain it please.

fluttershyk · Answer

@563blackghost did I do that right

563blackghost · Answer

Basically with factoring we simplify it down to its factors....

In this case we have $\large{81x^{2}}$...Now we know that $\Large{\sqrt{81}=9}$ Which means that $\Large{9 \times 9 =81}$ but we need to find it where it has $\large{x^{2}}$ now the only way to get that is if you multiply x by x so we would add and x to the 9's....so right now we have...

$\huge{(9x(blank))(9x (blank))}$

563blackghost · Answer

So 

$\huge{9x \times 9x = 81x^{2}}$

563blackghost · Answer

so we have that down already for our question but we still have to factor 25...what would multiply itself to equal 25?

ayanaortega · Answer

but i have to show my work

563blackghost · Answer

" To find the answer we would first analyze what factorization is....we know that we would have two equations that would multiply itself to equal the binomial...so to find the answer we would have to find a number that multiplies itself to equal $\large{81x^{2}}$ and the other $\large{25}$"

Now from knowing my times tables 9 is a number that multiples itself to equal 81 but we want $\large{81x^{2}}$....well we know that if we multiply x by x we would get $\large{x^{2}}$ so we would add an x to 9 and have....

$\LARGE{(9x ~blank)(9x ~blank)}$

ayanaortega · Answer

so we have to do (9x blank) (9x blank) first right

563blackghost · Answer

yup ^^ 

Now we need to determine a number that multiples itself to equal 25....

ayanaortega · Answer

5*5=25

563blackghost · Answer

Correct ^^

Now the 25 we have is a negative....and the only way to get a negative as an outcome when multiplying is by multiplying a negative by a positive so...

$\LARGE{-5 \times 5=-25}$

Now that we have determined this we would input $\large{-5}$ into one parenthesis and $\large{5}$ into the other....so our answer would be...

$\huge\color{Red}{(9x-5)(9x+5)=81x^{2}-25}$

ayanaortega · Answer

so in red is our answer right

563blackghost · Answer

Correct ^^

ayanaortega · Answer

thanks for helping me

563blackghost · Answer

np ^^