Polynomials - Multiplying Polynomials
Polynomials are made up of terms.
Terms - are a product of numbers and/or variables.
Terms - are connected to each other by addition or subtraction.
Polynomial calls any of the following;
monomial has one term, such as 3x2.
binomial has two terms, such as a2 − b2.
trinomial has three terms, such as ax2 + bx + c.
If more than three terms, just call it polynomial
Multiplying polynomials can take several different forms based on what we are multiplying.
Multiplying coefficients, then add the exponents of the same variables.
Multiply by Distributing, e.g.
2a(3x + 2y - z) = distribute 2a to all terms inside parentheses.
Answer = 6ax + 4ay - 2az
Multiply by FOIL, e.g.
(a - b) (x - y) F - evaluate both FIRST variables
ax O - evaluate both OUTSIDE variables
ax - ay I - evaluate both INSIDE variables
ax - ay - bx L - finally, evaluate both LAST variables
Answer = ax - ay - bx - ay
Multiplying in rows, e.g.
(4a + b - 3c) (3x + 2x) arrange like multiplying arithmetic;
4a + b - 3c
3x + 2x
+ 8ax + 2bx - 6cx
+ 12ax + 3bc - 9cx
20ax + 5bx - 15cx = answer
Polynomials are made up of terms.
Terms - are a product of numbers and/or variables.
Terms - are connected to each other by addition or subtraction.
Polynomial calls any of the following;
monomial has one term, such as 3x2.
binomial has two terms, such as a2 − b2.
trinomial has three terms, such as ax2 + bx + c.
If more than three terms, just call it polynomial
Multiplying polynomials can take several different forms based on what we are multiplying.
Multiplying coefficients, then add the exponents of the same variables.
Multiply by Distributing, e.g.
2a(3x + 2y - z) = distribute 2a to all terms inside parentheses.
Answer = 6ax + 4ay - 2az
Multiply by FOIL, e.g.
(a - b) (x - y) F - evaluate both FIRST variables
ax O - evaluate both OUTSIDE variables
ax - ay I - evaluate both INSIDE variables
ax - ay - bx L - finally, evaluate both LAST variables
Answer = ax - ay - bx - ay
Multiplying in rows, e.g.
(4a + b - 3c) (3x + 2x) arrange like multiplying arithmetic;
4a + b - 3c
3x + 2x
+ 8ax + 2bx - 6cx
+ 12ax + 3bc - 9cx
20ax + 5bx - 15cx = answer
