Quadratic Polynomial Expansion in Algebra
Polynomials come in two forms. They can be expanded such as ax2+bx+c or they can be factored: (dx-e)(fx+g) where a,b,c,d,e,f,g are coefficients or constants while x is the variable. This post shows how to go from factored form to expanded form in the following examples:
Example 1:
(x+2)(x+2) = x(x+2)+2(x+2)
= x2+2x+2x+4
= x2+4x+4
Example 2:
(x+3)(x+5) = x(x+5)+3(x+5)
= x2+5x+3x+15
= x2+8x+15
The next example uses foil which can be used on any quadratic polynomial. Foil stands for first, outside, inside and last which is the order that terms are multiplied.
Example 3:
(x+2)(x+8)
First: x2
Outside: 8x
Inside: 2x
Last: 16
| First + Outside + Inside + Last | = x2+8x+2x+16 |
| = x2+10x+16 |
All of the examples use the Law of Distribution.