In algebra special products and the questions says to factor the equation 200x^2-18 and I don't get how to.
factor out a two, then what remains will be the difference between two perfect squares.
I got as far as this 2(100x-3)^2 and that isn't right becaus ethe 18 has to be negative.
2(100x^2-9)
Now, what is (10x-3)(10x+3) ?
Review the factors for a difference of two squares (a^2-b^2).
To factor the equation 200x^2 - 18, we can follow these steps:
1. Factor out a common factor of 2: 2(100x^2 - 9).
2. Recognize that 100x^2 - 9 is a difference of two squares. It can be written as (10x)^2 - 3^2.
3. Apply the formula for factoring a difference of two squares: (a^2 - b^2) = (a - b)(a + b).
In this case, a = 10x and b = 3.
So, (10x)^2 - 3^2 can be factored as (10x - 3)(10x + 3).
Therefore, the factorization of 200x^2 - 18 is 2(10x - 3)(10x + 3).
To factor the equation 200x^2 - 18, we can follow the steps you mentioned.
First, we can factor out a 2 from both terms:
2(100x^2 - 9)
Now, we need to look for a difference of squares in the expression (100x^2 - 9). A difference of squares occurs when we have an expression in the form (a^2 - b^2). In this case, a is 10x and b is 3.
So, (100x^2 - 9) can be written as (10x)^2 - (3)^2.
Using the formula for a difference of squares, we can rewrite it as:
(10x - 3)(10x + 3)
Therefore, the factored form of the equation 200x^2 - 18 is 2(10x - 3)(10x + 3).