Factor completely.
25, x, squared, minus, 81
25x^2−81
To factor the expression 25x^2 - 81 completely, we can rewrite it as a difference of squares:
25x^2 - 81 = (5x)^2 - 9^2
Now, we can factor the difference of squares:
(5x)^2 - 9^2 = (5x + 9)(5x - 9)
Therefore, the completely factored expression is (5x + 9)(5x - 9).
To factor the expression 25x^2 - 81 completely, you can split the middle term using the difference of squares formula.
The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).
In our expression, we have 25x^2 - 81, where 25x^2 is the square of 5x and 81 is the square of 9.
So, we can rewrite the expression as (5x)^2 - 9^2.
Using the difference of squares formula, we get:
(5x + 9)(5x - 9).
Therefore, the expression 25x^2 - 81 factors completely as (5x + 9)(5x - 9).
To factor the expression 25x^2 - 81 completely, we need to rewrite the expression as a difference of squares. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).
In our case, a^2 is 25x^2 and b^2 is 81. Taking the square root of both a^2 and b^2, we get a as 5x and b as 9. Therefore, our expression can be rewritten as:
(5x + 9)(5x - 9)
And that is the complete factored form of 25x^2 - 81.