Question

Evaluate the followin
(1) (99)^3
solve please​

Answer 1

Explanation:

We have,

(99)

3

=(100−1)

3

We know that

(a−b)

3

=a

3

−b

3

−3ab(a−b)

Therefore,

=(100)

3

−1

3

−3×100×1×(100−1)

=1000000−1−300(100−1)

=1000000−1−30000+300

=970299

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Here ,given (99)^3

we can also write 99 as (100-1)

so,we can also write (99)^3 as (100-1)^3

Here ,this identity is used:

$\bold{\boxed{\purple{{(x - y)}^{3} = {x}^{3} + {y}^{3} -3xy(x-y)}}}$

$= > {(100 - 1)}^{3} = {(100)}^{3} + {(1)}^{3} - 3(100)(1)(100 - 1)$

$= 1000000 + 1 - 300(100 - 1)$

$= > 1000000 + 1 - 30000 + 300$

$= > 1000001 - 30000 + 300$

$= > 970001 + 300 ={\red{ 970301}}$

ㅤㅤㅤㅤㅤㅤㅤ

Other related identity:-

$\bold{\boxed{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

$\bold{\boxed{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3 {x}^{2} y + 3x {y}^{2}}}$

$\bold{\boxed{{x}^{2} + {y}^{2} = (x + y)(x - y)}}$

$\bold{\boxed{{x}^{3} + {y}^{3} = (x + y)[{x}^{2} - xy + {y}^{2} ]}}$