polynomials

Question

(2/3x+4)(9x-12)

Answer 1

Hi Karla, I am not sure what you want to know about these two binomials. You can multiply them to get a polynomial.

 

Polynomial:

 

(2/3 x + 4) * (9x - 12)

 

We can use the distributive law a(b + c) = ab + ac, to get the answer.

 

We can use FOIL to get the answer.

 

Lets do both:

 

The distributive law:

 

We need to use the distributive law twice. First time:

 

Distribute the 2/3x through (9x - 12)

 

2/3 x * 9x - 2/3 x * 12

 

18/3x² - 24/3x = 6x² - 8x

 

Distribute the 4 through (9x - 12)

 

4 * 9x - 4 * -12 = 36x - 48

 

Combine the results of the two distributions:

 

6x² - 8x + 36x - 48

 

Combine like terms:

 

6x² + 28x - 48

 

Solve using FOIL:

 

F(irst terms of each binomial)    = 2/3x * 9x = 18/3 x² = 6x²

O(utter terms of each binomial) = 2/3x * - 12 = -24/3 x = -8x

I(nner terms of each binomial)  = 4 * 9x = 36x

L(ast terms of each binomial)    = 4 * -12 = -48

 

This gives: 6x² -8x +36x - 48 or:

 

6x² + 28x - 48

 

These two methods give the same answer:

 

Is this what you were looking for?