This week we learned how to multiply polynomials in several different ways. In order to multiply polynomials, you need to understand the distributive property and the multiplication exponent law, but I will explain them when they come up. I this I will explain how to multiply a trinomial (3 terms) by a binomial (2 terms) in 2 ways. The example I will be solving is (5x2-3x+6)(4x+5)
Way 1: algebraically
First I can start with expanding. Each term in the first bracket will multiply into terms in the second, because of the distributive property. This is what the equation would look expanded:
5x2(4x)+5x2(5)-3x(4x)-3x(5)+5(4x)+5(5)
Know I can do the individual multiplication:
20x3+25x2-12x2-15x+20x+20
The reason 5x2(4x)=20x3 is according to the multiplication exponent law. There in an invisible exponent of 1 on the 4x.
Before I combine like terms I like to organize my equation to make things easier for myself. I organize the equation by like terms then I combine. This equation is already organized so I can skip that step.
Like terms combined: 20x3+13x2+5x+20
Way 2: visually
(5x2-3x+6)(4x+5)
You start with making a box with lines separating it to the number of terms
Then you fill in the polynomials to their respective sides. put each term on a line like this
| 4x | 5 | |
| 5x2 | ||
| -3x | ||
| 6 |
Then I would do the multiplication in the individual squares
| 4x | 5 | |
| 5x2 | 20x3 | 25x2 |
| -3x | -13x2 | -15x |
| 6 | 24x | 30 |
Know I can right out the hole equation and combine like terms.
Written out: 20×3+25×2-12×2-15x+20x+20
Like terms combined: 20×3+13×2+5x+20