How does '(3x+5)(2x-1)' equal '6x^2+7x-5'?

[Mizuki]

Alright (3x + 5)(2x - 1) = 6x^2-3x+10x-5
[ 6x^2+7x-5 ] <- final answer

Those were the notes on that type of problem, and it makes no sense at all to me. How would you go about coming up with those numbers? I keep guessing but it's all just too confusing... ._. Please help, I couldn't bear failing another test!

 

[stapel]

Are you asking how to get from the original product to the first polynomial, or how to get from the first polynomial to the simplified form? That is, are you needing lessons on adding polynomials or on multiplying polynomials?

Thank you.

Eliz.

 

[Thor]

Hi Mizuki!
Well, to multiply polynomials, we use the FOIL method. First Outer, Inner Last.

(3x + 5)(2x - 1) = 6x^2-3x+10x-5

So taking your basic equation of (3x+5)(2x-1), we take the first two variables in each parenthasis: 3x, and 2x, and multiply them together to get 6x^2.

Then we take the first variable in the first parenthasis, and multiply it by the last variable in the second, so it would be 3x * -1, to get a -3x.

After that, we use the two inner variables, or the second variable in the first parenthasis (5) and multiply by the first variable of the second (2x) to produce 10x.

After that, all we do is multiply the last variables in each parenthasis (5) and (-1), to get -5.

We end up with 6x^2-3x+10x-5 after it is all arranged. Then we simplify by adding the x variables together to get 7x, making the entire equation: 6x^2+7x-5.

Is that what you were looking for?