Factor completely.
121, minus, 81, x, squared
121−81x^2
To factor completely, let's first consider the formats of the given terms:
121 is a perfect square (11²).
81x² can be factored as (9x)².
Using these factors, we can rewrite the expression as:
(11-9x)(11+9x)
So, 121 - 81x² factors completely as (11-9x)(11+9x).
To factor the expression 121 - 81x^2 completely, we need to recognize it as the difference of squares and apply the corresponding formula. The difference of squares formula is:
a^2 - b^2 = (a + b)(a - b)
In this case, a = 11 and b = 9x. So we can rewrite the expression as:
(11)^2 - (9x)^2 = (11 + 9x)(11 - 9x)
Therefore, the expression 121 - 81x^2 can be factored completely as (11 + 9x)(11 - 9x).
To factor the expression 121 - 81x^2 completely, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b).
In this case, we have 121 - 81x^2. Notice that both 121 and 81x^2 are perfect squares, with 121 being 11^2 and 81x^2 being (9x)^2.
Using the difference of squares formula, we can rewrite the expression as follows:
121 - 81x^2 = (11)^2 - (9x)^2.
Now, we can apply the difference of squares formula:
(11 + 9x)(11 - 9x).
Therefore, the expression 121 - 81x^2 factors completely to (11 + 9x)(11 - 9x).