Download One and Two digit Addition and Subtraction - Perfect Math

Polynomial Basics
Peter Gibby
Polynomial
• A polynomial has multiple variables that we
cannot add together, such as x and y, or x and
x2
• We can actually have as many variables and
exponents of variables as we can fit.
• There are ways to add, subtract, multiply, and
divide these still even if the variables do not
add up.
Examples
•
•
•
•
4x+2y
2x2-x-y+y2
a+2b+3c+4d+5e+6f
x6+4zx5+3yx11-9xz+5x2+x6y2z+xy6
Addition
• Adding or subtracting these is like adding and
subtracting different values. We just group the
“like terms” (terms with the same variables
and exponents) together then add or subtract.
• 4x2y+2xy-3xy2+2x2y+2xy2-5xy
• 4x2y+2x2y+2xy-5xy-3xy2+2xy2
• 6x2y-3xy-xy2
Multiplication
• We have done this before actually, just on a
smaller scale. We used FOIL for quadratics. We
do something similar. If it is 2 values
multiplied by 2 values, we do FOIL. If its more,
then we distribute each value to the other
group.
Example
• (x+y-z)(2x2-yz+y+z)
• x(2x2-yz+y+z)+y(2x2-yz+y+z)-z(2x2-yz+y+z)
• 2x3-xyz+xz+2x2y-y2z+y2+yz-2x2z+yz2-yz-z2
– Now we combine like terms
• 2x3-xyz+xz+2x2y-y2z+y2+yz-2x2z+yz2-yz-z2
• There are no like terms, so this is as simple as we
will get it.
• Notice that FOIL is just distributing with two
numbers.