To multiply (x + 6)(x - 2) through, apply the law of distributivity a(b - c) = ab - ac where a = x + 6, b = x and c = 2. Then apply distributivity two times more.
I have not taken algebra in 20 years, and have an algebra class left to complete my associates. Ive been reviewing like crazy, but much of this is still stumping me and I feel behind so I'll be coming in here a bit to see if I can get help, and find a tutor at the college. Im making progress, but its SLOW, and PAINFUL, and time-consuming. Have to do this when my kids are at school in order to have peace to study.
Anyway, stuck on something here, I'll give you part of the problem below:
Code:3 1 4 --- + --- = ----- X+6 x-2 x(2) + 4x - 12
The section x(2) + 4x - 12 in the book is show factored to (x+6)(x-2)
This is done to also find the LCD.
I dont understand how it got to (x+6)(x-2)??
One of the most important skills in mathematics is the ability to make a substitution of a concrete expression for a variable into another expression. For example, to substitute a concrete expression x + 6 for a variable into the law of distributivity a(b - c) = ab - ac, replace with x + 6. The result is (x + 6)(b - c) = (x + 6)b - (x + 6)c. Then substitute x for b and 2 for c in the equality just obtained.
Your quadratic looks like this: . Can you see that it is of the form , with and ?
So to factorise, you are looking for two numbers which multiply to give -12 and add to give 4. If you're good with your rules of numbers and times tables, you will know straight away that the two numbers are 6 and -2.
So that means .