Question

Evaluate each of the following:

(i) 111³ − 89³

(ii) 46³+34³

(iii) 104³ + 96³

(iv) 93³ − 107³

Answer 1

In the given problem, we have to find the value of numbers

(i) Given

We can write as

We shall use the identity

Here

${111}^3-{89}^3={\left(100+11\right)}^3-{\left(100-11\right)}^3$

Hence the value of is

(ii) Given

We can write as

We shall use the identity

Here

${46}^3+{34}^3={\left(40+6\right)}^3+{\left(40-6\right)}^3$

Hence the value of is

(iii) Given

We can write as

We shall use the identity

Here

${104}^3+{96}^3={\left(100+4\right)}^3+{\left(100-4\right)}^3$

Hence the value of is

(iv) Given

We can write as

We shall use the identity

Here

Hence the value of is .