<h2>
Question:</h2>
Evaluate using a suitable identity: (997)³
<h2>
Answer:</h2>
991026973
<h2>
Step-by-step explanation:</h2>
Given:
(997)³
To solve this using an appropriate identity;
i. <em>Rewrite by splitting the value in bracket (997) into a difference of two numbers. i.e</em>
(997)³ = (1000 - 3)³
<em>ii. Use the appropriate identity</em>
Since the split from (i) above gave a cube of the difference of two numbers, we can apply the following identity for finding the cube of the difference of two numbers;
(a - b)³ = a³ - b³ - 3ab(a - b)
In this case;
a = 1000
b = 3
<em>(iii) Substitute the values of a and b into the identity equation and solve;</em>
(1000 - 3)³ = 1000³ - 3³ - 3(1000)(3)(1000 - 3)
(1000 - 3)³ = 1000000000 - 27 - 9000(997)
(1000 - 3)³ = 1000000000 - 27 - 8973000
(1000 - 3)³ = 991026973
Therefore,
(997)³ = 991026973
