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 (5x^{2}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:
5x^{2}(4x)+5x^{2}(5)3x(4x)3x(5)+5(4x)+5(5)
Know I can do the individual multiplication:
20x^{3}+25x^{2}12x^{2}15x+20x+20
The reason 5x^{2}(4x)=20x^{3} 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: 20x^{3}+13x^{2}+5x+20
Way 2: visually
(5x^{2}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
Then I would do the multiplication in the individual squares

4x 
5 
5x^{2} 
20x^{3} 
25x^{2} 
3x 
13x^{2} 
15x 
6 
24x 
30 
Know I can right out the hole equation and combine like terms.
Written out: 20×3+25×212×215x+20x+20
Like terms combined: 20×3+13×2+5x+20