Question

Without actually calculating the cubes find 2(0.3)³+(0.4)³+(0.5)³+(-0.7)³+(-0.8)³


plzzz solve with clear steps

Answer 1

We have 2 ( 0. 3 )3 + ( 0. 4 )3 + ( 0. 5 )3 + ( - 0. 7 )3 + ( - 0. 8 )3

Now we write it As :

⇒2 ( 0. 3 )3 + ( 0. 4 )3 + ( 0. 5 )3 - ( 0. 7 )3 - ( 0. 8 )3 ( As we know ( - 1 )3 = - 1 )

⇒2 ( 0. 3 )3 + ( 0. 4 )3 - ( 0. 7 )3 + ( 0. 5 )3 - ( 0. 8 )3

⇒2 ( 0. 3 )3 + ( 0. 4 - 0. 7 ) [ ( 0. 4 )2 + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + ( 0. 5 - 0. 8 ) [ ( 0. 5 )2 + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ] ( As we know ( a3 - b3 ) = ( a - b ) ( a2 + b2 + ab ) )

⇒2 ( 0. 3 )3 + ( - 0. 3 ) [ ( 0. 4 )2 + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + ( - 0.3 ) [ ( 0. 5 )2 + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ]

⇒- ( 0 . 3 ){ - 2 ( 0. 3 )2 + [ ( 0. 4 )2 + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + [ ( 0. 5 )2 + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ] }

⇒- ( 0 . 3 ){ [ ( 0. 4 )2 -( 0. 3 )2 + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + [ ( 0. 5 )2 -( 0. 3 )2 + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ] }

⇒- ( 0 . 3 ){ [ ( 0. 4 - 0. 3)( 0. 4 + 0. 3) + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + [ ( 0. 5 - 0. 3)( 0. 5 + 0. 3) + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ] } ( As we know ( a2 - b2 ) = ( a -b ) ( a + b ) )

⇒- ( 0 . 3 ){ [ ( 0. 1 )( 0. 7 ) + ( 0. 7 )2 + ( 0. 4 )( 0. 7 ) ] + [ ( 0. 2 )( 0. 8 ) + ( 0. 8 )2 + ( 0. 5 )( 0. 8 ) ] }

⇒- ( 0 . 3 ){ ( 0. 7 ) [ ( 0. 1 ) + ( 0. 7 ) + ( 0. 4 ) ] + ( 0. 8 ) [ ( 0. 2 ) + ( 0. 8 ) + ( 0. 5 ) ] }

⇒- ( 0 . 3 ){ ( 0. 7 ) [ 1. 2 ] + ( 0. 8 ) [ 1.5 ] }

⇒- ( 0 . 3 ){ 0.84 + 1.2 }

⇒- ( 0 . 3 ){ 2.04 }

⇒- 0. 612 ( Ans )