Question

Find the value of 12³–11³​

Answer 1

Answer:

397

Step-by-step explanation:

12×12×12-11×11×11

=1728-1331

=397

Answer 2

Given Question :-

• Find the value of 12³–11³

$\large\underline{\bold{Solution :- }}$

We know the identity,

$\rm :\longmapsto\: \boxed{ \bf {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2}) }$

So,

$\rm :\longmapsto\: {12}^{3} - {11}^{3}$

$\rm :\longmapsto\: = \: (12 - 11)( {12}^{2} + 12 \times 11 + {11}^{2} )$

$\rm :\longmapsto\: = \: (1)(144 + 132 + 121)$

$\rm :\longmapsto\: = \: 397$

$\rm :\implies\: \boxed{ \bf \: {12}^{3} - {11}^{3} = 397 }$

Additional Information :-

More algebraic identities :-

$(1). \: \boxed{ \bf \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}$

$(2). \: \boxed{ \bf \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}$

$(3). \: \boxed{ \bf \: {x}^{2} - {y}^{2} = (x + y)(x -y) }$

$(4). \: \boxed{ \bf \: {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}$

$(5). \: \boxed{ \bf \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)}$

$(6). \: \boxed{ \bf \: {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}$

$(7). \: \boxed{ \bf \: {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )}$

$(8). \: \boxed{ \bf \: (x + y + z)^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx)}$

$(9). \: \boxed{ \bf(x + a)(x + b) = {x}^{2} + x(a + b) + ab}$

$(10). \boxed{ \bf \: {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2}) }$

$(11). \: \boxed{ \bf \: {(x + y)}^{2} + {(x - y)}^{2} = 4xy }$