# Thread: How do I simplify this since it's too long to use foil?

1. ## How do I simplify this since it's too long to use foil?

The problem is: (3x^2+5x+4)(-5x^2-x+3)

Would I distribute 3x^2 to -5x^2, then to -x, and then to 3, and then do the same with 5x and 4?

I'm just kinda confused because there are "+" signs within the parenthesis, but not in between them. That's throwing me off for some reason. I can't remember how you do all the different types of these problems (like ones that are multiplication, versus adding, etc...)

2. Hello, deathtolife04!

The problem is: .$\displaystyle (3x^2+5x+4)(-5x^2-x+3)$

Would I distribute $\displaystyle 3x^2$ to $\displaystyle -5x^2$, then to $\displaystyle -x$, and then to $\displaystyle 3$
and then do the same with $\displaystyle 5x$ and $\displaystyle 4$? . . . . Yes!
In general, we multiply each term in the first polynomial by each term in the second.
. . Don't let the signs confuse you . . . just "bring them along".

We wil have: .$\displaystyle (3x^2)(-5x^2)\;\;\;(3x^2)(-x)\;\;\;(3x^2)(3)\;\;\;(5x)(-5x^2)\;\;\;(5x)(-x)\;\;\;(5x)(3)$ . $\displaystyle (4)(-5x^2)\;\;\;(4)(-x)\;\;\;(4)(3)$

Then combine these products: .$\displaystyle -5x^4 - 3x^3 + 9x^2 - 25x^3 - 5x^2 + 15x - 20x^2 -4x + 12$

. . $\displaystyle = \;-15x^4 - 28x^3 - 16x^2 + 11x + 12$