Question

Find the binomial theorem of ,( 2x-5)⁴

Answer 1

Step-by-step explanation:

Pascal’s triangle uses powers starting from 0. So since you need the 4th power, it will be the row that is

1 4 6 4 1

Knowing that row, the expansion is

1(2x)^4 +4(2x)^3(-5)^1 + 6(2x)^2(-5)^2 + 4(2x)^1(-5)^3 + 1(2x)^0(-5)^4

The expansion has 3 parts:

1) the coefficients from the triangle

2) that first term (2x) and its exponents

3) the last term (-5) and its exponents

Notice that each term starts with the number from Pascal’s Triangle, then the first term that you need to expand and then the last term you need to expand. All the powers add up to 4.

The (2x) term has exponents going from 4 down to 0. The (-5) term has exponents going up from 0 to 4.

Another check to be sure you are on the correct row is that the 4 is the 2nd term in the expansion.