Steps to Expanding a binomial

A binomial is a polynomial equation with two terms joined by a plus or minus, and in order to expand binomials, you can use the binomial theorem to write the expansion of a binomial.

Example 1

Expand: (3m-2)^4

Step 1: 1ab + 4ab + 6ab + 4ab + 1ab

Step 2: 1a^4b^0 + 4a^3b^1+ 6a^2b^2 + 4a^1b^3 +1a^0b^4

Plug in exponents starting from the exponent in the equation

write out ab along with the coefficients

Example 1 Continued

Step 3: (3m)^4+4(3m)^3(-2)+6(3m)^2(-2)^2+4(3m)(-2)^3+(-2)^4

Plug in numbers/variables into a and b

Step 4: 81m^4-216m^3+216m^2-96m+16

Get rid of exponent and simplify

Example 2

Expand (3x-y)^6

Step 1: 1ab 6ab 15ab 20ab 15ab 6ab 1ab

Step 2: 1a^6b^0 + 6a^5b + 15a4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 a^0b^6