Questions
Will the FOIL Method work for multiplications that are not binomial times binomial?
The general topic will (multiply each term by each term), but the exact FOIL will not be the same.
FOIL?
First terms
Outer terms
Inner terms
Last terms
(x + 5)(x + 2)
x^2 + 7x + 10
When multiplying two linear binomials, what is the result?
A quadratic expression
Quadratic expression?
ax^2 + bx + c
(y - 2)(y - 4)
y^2 - 6y + 8
Do you multiply the terms within one parenthesis?
No
Polynomial?
Multiple terms that can't be combined
4n^2 + 39n + 27
What would happen if you multiplied two polynomials whose terms had variables for exponents.
Nothing different! When multiplying exponents, you add the exponents as long as the base is the same (ex. x^6 * x^7 = x^13, but you can't do x^9 * y^3)
Binomial?
Two terms that cannot be combined?
(2a - 9)(3a^2 + 4a - 4)
6a^3 − 19a^2 − 44a + 36
What are other ways you can multiply polynomials?
You can rainbow it, you can set it up vertically, you can distribute, etc.
Bases?
The variable and exponent (if it's there)
5x^4 − 17x^3 + 9x^2 + 31x − 20