Question

(a-b)^3= ?

(step by step answer please.)



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Answer 1

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.

Answer 2

Answer:

The (a - b)3 formula is also known as one of the important algebraic identities.

It is read as a minus b whole cube.

Its (a - b)3 formula is expressed as (a - b)3 = a3 - 3a2b + 3ab2 - b3

How To Simplify Numbers Using the (a - b)3 Formula?

Let us understand the use of the (a - b)3 formula with the help of the following example.

Example: Find the value of (20 - 5)3 using the (a - b)3 formula.

To find: (20 - 5)3

Let us assume that a = 20 and b = 5.

We will substitute these in the formula of (a - b)3.

(a - b)3 = a3 - 3a2b + 3ab2 - b3

(20-5)3 = 203 - 3(20)2(5) + 3(20)(5)2 - 53

= 8000 - 6000 + 1500 - 125

= 3375

Answer: (20 - 5)3 = 3375.