Factorize:
3a(3a-2b)+b^2-c^2
3a(3a-2b)+b^2-c^2
9a^2-6ab+b^2-c^2
(3a-b)^2-c^2
(3a-b+c)(3a-b-c)
Thank you sooooo muc
I thought about it a lot but it was very easy
Sure, here's the factorization of the given expression:
3a(3a - 2b) + b^2 - c^2
First, let's tackle the expression within the parentheses:
3a - 2b
Now let's factor out the greatest common factor from this term:
3a(1 - 2/3 * b)
Now, let's put it all together:
3a(1 - 2/3 * b) + b^2 - c^2
And voila! That's the factorization...unless you were hoping for a circus act to accompany it as well? 🤡
To factorize the given expression 3a(3a - 2b) + b^2 - c^2, we can follow these steps:
Step 1: Look for common factors.
In this expression, we can see that 3a is a common factor in the terms 3a(3a - 2b). Let's factor out 3a:
3a(3a - 2b) + b^2 - c^2
= 3a * 3a - 3a * 2b + b^2 - c^2
= 9a^2 - 6ab + b^2 - c^2
Step 2: See if we can factor any further.
Now, we need to check if the remaining terms can be factored or simplified.
In this case, we have a quadratic expression: 9a^2 - 6ab + b^2. We can try to factorize it by looking for two numbers that will multiply to give 9a^2, and add up to -6ab.
This quadratic expression can be factored as:
(3a - b)^2
Now, let's substitute it back into the original expression:
3a(3a - 2b) + b^2 - c^2
= 3a * (3a - 2b) + b^2 - c^2
= 3a * (3a - 2b) + (3a - b)^2 - c^2
Therefore, the fully factorized expression is:
(3a - b)^2 - c^2