Question

Find the value of 2.7 ³ - 1.6 ³ - 1.1 ³ using a suitable identity.

Answer 1

Answer:

14.256

See details below

Step-by-step explanation:

2.7 ³ - 1.6 ³ - 1.1 ³

= (2.7 ³  - 1.1 ³) - 1.6 ³   expand difference of two cubes

= (2.7 - 1.1)*(2.7^2 + 2.7*1.1 + 1.1^2) - 1.6 ³    

= 1.6*(2.7^2 + 2.7*1.1 + 1.1^2) - 1.6 ³    factor out 1.6

= 1.6*(2.7^2 - 1.6^2 + 2.7*1.1 + 1.1^2)    expand difference of two squares

= 1.6*( (2.7 - 1.6)*(2.7 + 1.6) + 2.7*1.1 + 1.1^2)

= 1.6*( 1.1*4.3 + 2.7*1.1 + 1.1^2)    factor out 1.1

= 1.6*1.1* ( 4.3 + 2.7 + 1.1)

= 1.6*1.1*8.1    rearrange

= 1.6 * 8.1 * 1.,1

= 16 * 0.81 * 1.1

= (4*0.9)^2 * 1.1

= 3.6^2 * 1.1  

= 12.96 * 1.1              36*36=1296

= 14.256    

(to multiply by 1.1, mentally start from the right, add the left digit, carry if necessary)