Factor completely.
16, minus, 121, x, squared
16−121x^2
To factor the expression completely:
Step 1: Rewrite 16 as a perfect square.
16 = 4^2
Step 2: Write the expression with the square term in front.
-121x^2 + 16
Step 3: Rewrite -121 as a perfect square multiplied by -1.
-121 = (-11)^2 * -1
Step 4: Rewrite the expression using the perfect square.
-121x^2 + 16 = (-11x)^2 - 4^2
Step 5: Apply the difference of squares formula.
(-11x)^2 - 4^2 = (-11x + 4)(-11x - 4)
Therefore, the expression 16 - 121x^2 factors completely to (-11x + 4)(-11x - 4).
To factor the expression 16 - 121x^2, we can use the difference of squares formula.
The difference of squares formula states that if we have an expression in the form a^2 - b^2, we can factor it as (a + b)(a - b).
In this case, a^2 is 16 and b^2 is 121x^2. To find the values of a and b, we take the square root of each:
√16 = 4
√(121x^2) = 11x
So, the factored form of 16 - 121x^2 is (4 + 11x)(4 - 11x).
To factor the expression 16 - 121x^2 completely, we need to look for common factors in each term. In this case, there are no common factors among the terms.
However, we can notice that the expression follows a pattern called the difference of squares. The difference of squares formula states that for any two numbers, a and b, the expression a^2 - b^2 can be factored as (a + b)(a - b).
Using this formula, we can rewrite the expression as (4)^2 - (11x)^2. Now we can factor it using the difference of squares.
The factored form of 16 - 121x^2 is (4 + 11x)(4 - 11x).