Question

Evaluate using suitable identities 1000^3 - 999^3

Answer 1

Hey

Here is your answer,

a = 1000
b = 999

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

By using this identity,

(1000)^3 - (999)^3

= (1000-999) (1000^2 + 1000x999 + 999^2)

=(1) (1000000 + 999000 + 998001)

=2997001

Hope it helps you!

Answer 2

1000³ - 999³ = 2997001

Given :

The expression 1000³ - 999³

To find :

The value of the expression using suitable identity

Identity Used :

a³ - b³ = (a - b)³ + 3ab(a - b)

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

1000³ - 999³

Step 2 of 2 :

Find the value of the expression

We are aware of the identity that ,

a³ - b³ = (a - b)³ + 3ab(a - b)

Taking a = 1000 & b = 999 we get

1000³ - 999³

= (1000 - 999)³ + 3 × 1000 × 999 × (1000 - 999)

= (1)³ + 3 × 1000 × 999 × 1

= 1 + 2997000

= 2997001

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