Factor completely.
49, minus, 100, x, squared
49−100x^2
To factor the expression 49 - 100x^2, we first notice that the expression is in the form of "a^2 - b^2." This can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
In this case, a = 7 and b = 10x, so we can write the expression as:
(7 + 10x)(7 - 10x)
Therefore, the expression 49 - 100x^2 factors completely as (7 + 10x)(7 - 10x).
To factor completely, we need to find the common factors among the terms. In this case, the expression doesn't have any common factors other than 1.
So, the expression 49 - 100x^2 cannot be factored any further.
To factor the expression 𝑦 = 49 − 100𝑥^2 completely, we can start by recognizing that it is a difference of squares. We can rewrite the expression as follows:
𝑦 = 7^2 − (10𝑥)^2
Now, we have a difference of squares form: 𝑎^2 − 𝑏^2.
Using the formula for factoring a difference of squares, we get:
𝑦 = (𝑎 + 𝑏)(𝑎 - 𝑏)
In our case, 𝑎 = 7 and 𝑏 = 10𝑥. Substituting these values, we can factor 𝑦 as:
𝑦 = (7 + 10𝑥)(7 - 10𝑥)
Therefore, the expression 49 − 100𝑥^2 is factored completely as (7 + 10𝑥)(7 - 10𝑥).