Question

Find the cube of each of the following using (a + b)³ 109​

Answer 1

Answer:

109 cubed, (109)3, is the number you get when multiplying 109 times 109 times 109.

It can also be looked at as exponentiation involving the base 109 and the exponent 3.

The term is usually pronounced 3rd power of one hundred nine or one hundred nine cubed.

The cube of 109 is a perfect cube because the number is the product of the three equal integers 109.

It can be written as 109 × 109 × 109 or in exponential form.

Read on to learn everything about the number one hundred nine cubed, including useful identities.

(109)3 = 1,295,029

109 × 109 × 109 = 1,295,029

The sum and the differences of two cubes, for example with side length 109 and 108, can be calculated with the following formulas:

a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3

With a = 109, b = 108 and the equivalence we get:

(109)3 = 217 x (1092 – 109 × 108 + 1082) – 1083 = 217 x (11881 – 11772 + 11664) – 1259712 = 217 x 11773 – 1259712 = 1,295,029

a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3

With a = 109, b = 108 and the equivalence we get:

(109)3 = (1092 + 109 × 108 + 1082) + 1083 = 11881 + 11772 + 11664 + 1259712 = 1,295,029

As follows from (1), 109 cubed can be calculated from 108 cubed and 109 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3

(109)3 = (2 × 109 – 1) × (1092 – 109 + 1) – (108)3 = 217 × (11881 – 108) – 1259712 = 217 × 11773 – 1259712 = 1,295,029

Using the second formula 109 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1

(109)3 = 1083 + 3 × 1092 – 3 × 109 + 1 = 1259712 + 3 × 11881 – 3 × 109 + 1 = 1259712 + 35643 – 327 + 1 = 1,295,029

Step-by-step explanation:

A cube is a three-dimensional shape with 6 equal square faces.

Hence, a cube with side length 109 has an area of 1,295,029.