For my math project
Responses (3)
This does not require "expand" or "simplify, it requires "evaluate".
(9x - 1)(x - 4) - (3x + 1)(3x - 1) Add spaces to improve readability.
(9x - 1)(x - 4) Multiply each term in the first parentheses by each term in the second.
9x^2 - 36x - x + 4 <-- PARTIAL RESULT
(3x + 1)(3x - 1) Same thing.
9x^2 + 3x - 3x - 1 And don't forget the entire phrase is negative!
-9x^2 - 3x + 3x + 1 <-- PARTIAL RESULT
Now combine the partial results.
9x^2 - 36x - x + 4 - 9x^2 - 3x + 3x + 1
- 37x + 5 <-- ANSWER
Let's expand the two products of sums:
(9x - 1) (x - 4) = 9x^2 - 36x - x + 4 ;; and simplify it
9x^2 - 37x + 4.
Now we do the same with the other one. (Note that
(a + b) (a - b) reduces to a^2 - b^2, because the linear terms -ab + ab cancel out):
(3x + 1) (3x - 1) = 9x^2 - 1.
Now we subtract the two terms
(9x^2 - 37x + 4) - (9x^2 - 1) ;; Solve the parentheses. The minus-sign in front of the second term is just a shorthand for a factor of -1.
(9x^2 - 37x + 4) + (-1) (9x^2 - 1)
9x^2 - 37x + 4 - 9x^2 + 1 ;; Again, simplify
-37x + 5.