FIND THE GCF OF THE PRODUCT (3B+6)(2B-10)
SOLVE...
X^2=-6X
x(x+6)= 0
x = -6 or 0
it would = 0
help me solve this problem..
solve for W: 2L+2W=38
please and thank you!
To find the Greatest Common Factor (GCF) of the product (3B+6)(2B-10), we can use the distributive property to expand the product:
(3B + 6)(2B - 10) = 3B(2B) + 3B(-10) + 6(2B) + 6(-10)
= 6B^2 - 30B + 12B - 60
= 6B^2 - 18B - 60
Now, we can factor out the greatest common factor from the resulting expression:
GCF(6B^2 - 18B - 60)
First, look for common factors of all the coefficients. The greatest common factor here is 6:
6(B^2 - 3B - 10)
Now, we need to factor the expression inside the parentheses:
B^2 - 3B - 10
To factor this quadratic expression, we look for two numbers that multiply to give -10 and add to give -3. The numbers -5 and 2 fit this criteria:
B^2 - 3B - 10 = (B - 5)(B + 2)
Therefore, the fully factored expression is:
GCF(6B^2 - 18B - 60) = 6(B - 5)(B + 2)
Moving on to the second question:
To solve the equation x^2 = -6x, we can rearrange it to have one side equal to zero:
x^2 + 6x = 0
Next, we factor out the common factor, x:
x(x + 6) = 0
Now, we set each factor equal to zero and solve for x:
x = 0
x + 6 = 0
x = -6
Therefore, the solution to the equation x^2 = -6x is x = -6 or x = 0.
Finally, for the equation 2L + 2W = 38, we are solving for W.
To isolate W, we can start by subtracting 2L from both sides of the equation:
2W = 38 - 2L
Then, divide both sides of the equation by 2:
2W/2 = (38 - 2L)/2
Simplifying, we get:
W = (38 - 2L)/2
Therefore, the solution for W in terms of L is W = (38 - 2L)/2.
I hope this explanation helps you solve the problems. Let me know if you have any further questions!
To find the greatest common factor (GCF) of the product (3B+6)(2B-10), we need to factor it first.
Step 1: Start by multiplying the terms inside the parentheses:
(3B+6)(2B-10) = 6B^2 - 30B + 12B - 60
Step 2: Combine like terms:
6B^2 - 18B - 60
Now, let's solve the equation x^2 = -6x.
Step 1: Move all terms to one side of the equation:
x^2 + 6x = 0
Step 2: Factor out the common term 'x':
x(x + 6) = 0
Step 3: Set each factor equal to zero and solve for x:
x = 0 or x + 6 = 0
x = 0 or x = -6
For the equation 2L + 2W = 38, we need to solve for W.
Step 1: Move the 2L term to the other side of the equation:
2W = 38 - 2L
Step 2: Divide both sides of the equation by 2:
W = (38 - 2L) / 2
Therefore, the solution for W is W = (38 - 2L) / 2.