Question

what is the answer of (a+b)³
then ​

Answer 1

Answer:

what is the answer of (a+b)³

then

Answer 2

Answer:This is what is called a third order binomial. Two terms (bi) taken to the third power (exponent of 3).

Unless you want to go through the same process of distributing and multiplying terms over and over again for more complicated binomials, then it helps to know the binomial theorem.

Short of that, when the coefficients for the terms are 1, as they are for a and b (well the coefficient for b is really -1), it helps to remember Pascal’s Triangle to obtain the coefficients.

So, for a third order binomial expansion, the numbers on the related line on Pascal’s Triangle are: 1, 3, 3, 1. These represent the coefficients of each of the four terms of a cubic binomial expansion. And, since b is really - b, the sign will alternate from (+) to (-) for each term.

I won’t simplify the terms the first time, and I will include all coefficients, as well as every “a” and “b” in every single term, so you can hopefully see the pattern.

Thus:

(a - b)^3 = (1)(a^3)(b^0) - (3)(a^2)(b^1) + (3)(a^1)(b^2) - (1)(b^3)(a^0)

Notice the leading exponents match the numbers from Pascal’s Triangle.

Notice that when the exponent for ”b” is odd, the term has a (-) sign. If the exponent for “b” is even, the term has a (+) sign.

Also notice how the exponents for “a” reduce by 1 for each term, and the exponents for b increase by 1.

Also remember that (a^0) and (b^0) are just 1.

Simplified:

(a - b)^3 = (a^3) - 3(a^2)(b^1) + 3(a^1)(b^2) - (b^3)

Hope that gets you started. Reread — or read if you are being lazy and haven’t done so — about Pascal’s Triangle and the Binomial Theorem. I only showed you the answer. You need to know how to get it. So, you still have some work to do.

Now, get to work!