Hello.
Can you explain to me how to factor the following?
30x^2 - 48x
6x^2 + 7xy - 20y^2
Thank you.
Hello!
Certainly, I can help you factor the given expressions.
To factor a quadratic expression like 30x^2 - 48x, you need to find two binomials whose product is equal to the given expression. Here's how you can factor it:
Step 1: Look for the greatest common factor (GCF) of the coefficients.
In this case, the GCF of 30 and 48 is 6, and the GCF of x^2 and x is x. So, we can factor out 6x:
30x^2 - 48x = 6x(5x - 8)
Now, let's move on to factoring the second expression, 6x^2 + 7xy - 20y^2.
Step 1: Look for the common factors of the coefficients.
Here, there are no common factors among 6, 7, and 20.
Step 2: Look for pairs of terms whose coefficients multiply to give the product of the first and last terms (6 * -20 = -120).
In this case, we can look for two numbers whose product is -120 and sums to the coefficient of the middle term (7). The numbers that meet this criteria are -15 and 8.
Step 3: Rewrite the middle term (7xy) as the sum of the two terms we found in step 2 (-15xy and 8xy).
So, the expression becomes:
6x^2 - 15xy + 8xy - 20y^2
Step 4: Group the terms.
Now, we can group the first two terms and the last two terms:
(6x^2 - 15xy) + (8xy - 20y^2)
Step 5: Factor out the greatest common factor (GCF) from each group.
In the first group (6x^2 - 15xy), the GCF is 3x:
3x(2x - 5y)
In the second group (8xy - 20y^2), the GCF is 4y:
4y(2x - 5y)
Therefore, the factored form of 6x^2 + 7xy - 20y^2 is:
(3x + 4y)(2x - 5y)
I hope this helps!