Question

Factorie 125^3 -64² by suitable identity

Answer 1

$Given \: 125^{3} - 64^{2}$

$= 125^{3} - (4^{3})^{2}$

$= 125^{3} - (4^{2})^{3}$

$= 125^{3} - 16^{3}$

$= (125 - 16)(125^{2} + 125\times 16+ 16^{2})$

___________________

/* By Algebraic Identity */

a³ - b³ = (a-b)(a²+ab+b²)

___________________

$= 109( 15625 + 2000+ 256)$

$= 109 \times 17881$

$= 1949029$

Therefore.,

$\red{ Value \:of \: 125^{3} - 64^{2}} \green { = 1949029}$

•••♪

Answer 2

125³ - 64² = 1949029 .

Solution :-

=> (125)³ - (64)³

=> 125³ - (4²)³

=> 125³ - 16³

=> [ °.° a³ - b³ = (a - b) (a² + ab + b²) ]

=> (125)³ -(16)³ = (125-16) ( 125² + 125×16 + 16²)

=> (125)³ - (16)³ = 109 ( 15625 + 2000 + 256)

=> (125)³ - (16)³ = 109 (17881)

=> (125)³ - (16)³ = 1949029.

.° . (125)³ - (64)² = 1949029.

Some algebraic identities :-

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = ( a + b) ( a - b)

• (a+b)³ = a³ + 3a²b + 3ab² + b³

• (a - b)³ = a³ - 3a²b + 3ab² - b³

• a³ - b³ = (a - b) (a² + ab + b²)