Question

find the value of (96)^3​

Answer 1

96 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied.

96 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied.(96)^ 3 =(100−4) ^3

=3 C 0 (100) ^3 −3 C 1 (100) ^2 (4)+3 C 2 (100)(4) ^2 −3 C 3 (4) ^3

=(100)^ 3 −3(100) ^2 (4)+3(100)(4) ^2 −(4) ^3

=884736

hope it helps you ❤️

Answer 2

Answer:

$use \: identity \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3}$

${96}^{3} \\ = {(100 - 4)}^{3} \\ = {(100)}^{3} - 3 \times {(100)}^{2} \times 4 + 3 \times 100 \times {(4)}^{2} - {(4)}^{3} \\ = 1000000 - 120000 + 4800 - 64 \\ = 884736$