Factor completely.
49, minus, 100, x, squared
49−100x ^2
The expression 49−100x^2 cannot be factored further as it is already in its simplest form.
To factor the expression 49 − 100x^2 completely, we can use the difference of squares formula. The difference of squares formula states that for any two terms a^2 - b^2, it can be factored as (a + b)(a - b). In our expression, 49 is a perfect square (7^2), but 100x^2 is also a perfect square (10x)^2.
Therefore, we can rewrite the expression 49 − 100x^2 as (7 + 10x)(7 - 10x).
That is the factorized form of the expression 49 − 100x^2.
To factor the expression 49 - 100x^2 completely, we can start by recognizing that it follows the difference of squares pattern, which states that:
a^2 - b^2 = (a + b)(a - b)
In this case, the expression 49 - 100x^2 can be rewritten as (7)^2 - (10x)^2:
(7)^2 - (10x)^2
Now, we can use the difference of squares pattern to factor it:
((7) + (10x)) * ((7) - (10x))
Simplifying further will give us the fully factored expression:
(7 + 10x)(7 - 10x)
So, the expression 49 - 100x^2 factors completely to (7 + 10x)(7 - 10x).