Factoring and expanding polynomials

Question 0

Steps to subtracting polynomials

Answer 0

To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn “+” into “-“, and “-“ into “+”), then add as usual.

Question 1

Steps to add a polynomial

Answer 1

1. Identity like terms and group together.

Example: Add     (2x2 + 6y + 3xy)  ,   (3x2 - 5xy - x)   and   (6xy + 5)
Line them up in columns and add:
2x2 + 6y + 3xy
3x2          - 5xy - x
                  6xy     + 5

5x2 + 6y + 4xy - x + 5

Question 2

1 term x 1 term (monomial times monomial)

Answer 2

To multiply one term by another term, first multiply the constants, then multiply each variable together and combine the result.

Example: (2xy) (4y)= 24xy*y=8xy^2

Question 3

To multiply two polynomials:

Answer 3

1. multiply each term in one polynomial by each term in the other polynomial.
2. add those answers together, and simplify if needed.

Question 4

1 term × 2 terms (monomial times binomial)

Answer 4

Multiply the single term by each of the two terms, like this:

2x(x+3xy)= 2xx+2x3xy
= 2x^2+6x^2y

Question 5

2 term × 1 terms (binomial times monomial)

Answer 5

Multiply each of the two terms by the single term, like this:
(x^2-x) 3y = 3x^2-3xy

Question 6

2 terms × 2 terms (binomial times binomial)

Answer 6

Each of the two terms in the first binomial is multiplied by each of the two terms in the second binomial. That is 4 differrent multiplications.
(2x+3)(xz-a)= 2x^2z-2xa+3xz-3a

Question 7

2 terms × 3 terms (binomial times trinomial)

Answer 7

Multiply each term in the first polynomial by each term in the second polynomial. And then combine like terms.
Example: (x + 2y)(3x − 4y + 5)
= 3x2 − 4xy + 5x + 6xy − 8y2 + 10y
= 3x2 + 2xy + 5x − 8y2 + 10y