can someone help me understand how to solve this... i have no idea what to do! why are the letters in the problem?
factoring strategy
9x^2 + 4y^2
The letters represent unknowns. Here is some strategy:
What would give a product of 4? (2*2 or 4 *1)
What would give a product of 9? (3*3 or 9*1)
How would those values effect any xy term?
If your formula was 9x^2 - 4y^2, it would factor into (3x + 2y)(3x - 2y). Do you have a typo?
To solve the given problem, which involves factoring the expression 9x^2 + 4y^2, we need to understand a few key concepts.
1. Factoring: Factoring is the process of breaking down an expression into its simplest form by finding common factors that can be pulled out.
2. Difference of Squares: The given expression, 9x^2 + 4y^2, is a special case of factoring known as the difference of squares. The difference of squares takes the form a^2 - b^2, where a and b are variables or constants. This expression can be factored as (a + b)(a - b).
Now, let's apply these concepts to the given problem:
The expression 9x^2 + 4y^2 is not in the form of a^2 - b^2, so we can't directly apply the difference of squares.
However, by observing the given expression, we see that both terms, 9x^2 and 4y^2, are perfect squares. The square of 3x is 9x^2, and the square of 2y is 4y^2.
So, we can rewrite the expression as (3x)^2 + (2y)^2.
Now, our expression is in the form a^2 + b^2, which can be factored as (a + b)(a - b).
Applying this to our expression, we have:
(3x)^2 + (2y)^2 = (3x + 2y)(3x - 2y).
Therefore, the factored form of the expression 9x^2 + 4y^2 is (3x + 2y)(3x - 2y).
By following these steps and recognizing the difference of squares pattern, we can determine the factorization of the given expression.