+676 First you'd want to simply the numerator,
Factor m out of \(81m^3−25m. \)
Which results in \(\frac{m(81m^2−25)}{9m+5 }\)
Given that the Co-Efficent is 81, the pronumeral (m) is sqaured and 25 is also a Sqaure Number, you may Square Root all of the numerator to produce this: \(\frac{m((9m)^2−5^2)}{9m+5}\)
Factor using the difference of squares.
Producing: \(\frac{m(9m+5)(9m−5)}{9m+5 }\)
Reduce the expression by cancelling the common factors. (See the denominator, [9m+5] and the numerator [m(9m+5)]
\(m(9m−5) \)
Apply the distributive property.
\(m(9m)+m(−5)\)
Simplify
\(9m^2+(−5m)\)
A Note of Caution here, Make sure you understand that a Positive and a Negative form a NEGATIVE:
\(9m^2−\Leftarrow5m\)
Ignore the Arrow, it is just a means of Bolding or Stating something worth noting.
\(9m^2−5m\)
is your Answer.
Simplify the following:
(81 m^3-25 m)/(9 m+5)
Factor m out of 81 m^3-25 m:
m (81 m^2-25)/(9 m+5)
81 m^2-25 = (9 m)^2-5^2:
(m (9 m)^2-5^2)/(9 m+5)
Factor the difference of two squares. (9 m)^2-5^2 = (9 m-5) (9 m+5):
(m (9 m-5) (9 m+5))/(9 m+5)
Combine powers. (m (9 m-5) (9 m+5))/(9 m+5) = m (9 m-5) (9 m+5)^(1-1):
m (9 m+5)^1-1 (9 m-5)
1-1 = 0:
m (9 m-5) (9 m+5)^0
(9 m+5)^0 = 1:
Answer: |m(9m - 5)
