How do you factor #25x^2-81#?

Question

Eva Adamson · Accepted Answer

The answer is: #x = 9/5# You first move the #-81# to the other side of the "equal" sign, it'll become positive instead of negative. #25x^2 = 81# The square root of each side of the equation is then obtained. #sqrt(25x^2) = sqrt81# The square roots are:
#25 = 5 xx 5#
#x^2 = x xx x#
#81 = 9 xx 9# This is how our equation looks when we apply this. #5x = 9# We divide each side by five. #(5x)/5 = 9/5# This cancels both 5 on the #x# side. #(cancel(5)x)/(cancel(5)) = 9/5# And thus, we arrive at our response: #x = 9/5#

Eva Adamson · Answer

You should realize that we will almost certainly use the Sum or Difference of Squares Identities when you see the numbers 25 and 81.

Given the negative sign, the Difference of Squares Identity will be applied.

It says #color(blue)(a^2 - b^2 = (a+b)(a-b)#

We can write the expression as# (5x)^2 - 9^2#

# =color(green)( (5x+9)(5x - 9)# is the factorised form

Ethan Adkins · Answer

undefined To factor $25x^2 - 81$, you can use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$. In this case, $25x^2$ is the square of $5x$ and $81$ is the square of $9$.

So, $25x^2 - 81$ can be factored as $(5x + 9)(5x - 9)$.

Abigail Allen · Answer

undefined To factor the expression $25x^2 - 81$, you can use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$.

In this case, $a = 5x$ and $b = 9$. So, applying the formula:

$25x^2 - 81 = (5x + 9)(5x - 9)$.

Therefore, the factored form of $25x^2 - 81$ is $(5x + 9)(5x - 9)$.