Given, x + 5 3 Comparing x + 5 3 with a + b 3 , we get a = 3 m and b = 5 . a + b 3 = a 3 + b 3 + 3 a b a + b x + 5 3 = x 3 + 5 3 + 3 × 5 × x ( x + 5 ) = x 3 + 125 + 15 x 2 + 75 x Thus, x + 5 3 = x 3 + 125 + 15 x 2 + 75 x

Given algebraic expression = y - 2 3 Use the standard algebraic identity ( a - b ) 3 = a 3 - b 3 - 3 a b a - b to find y - 2 3 . Compare ( y - 2 ) 3 with ( a - b ) 3 , we get a = y and b = 2 . So, y - 2 3 = y 3 - 2 3 - 3 × y × 2 y - 2 ⇒ ( y - 2 ) 3 = y 3 - 2 3 - 6 y y - 2 ⇒ ( y - 2 ) 3 = y 3 - 8 - 6 y 2 + 12 y Hence, the expanded form of y - 2 3 = y 3 - 6 y 2 + 12 y - 8

We have to expand 3 + m 3 Comparing ( 3 + m ) 3 with ( a + b ) 3 we have a = 3 , b = m ( a + b ) 3 = a 3 + 3 a 2 b + 3 ab 2 + b 3 ( 3 + m ) 3 = 3 3 + 3 ( 3 ) 2 ( m ) + 3 ( 3 ) m 2 + m 3 = 27 + 27 m + 9 m 2 + m 3 = m 3 + 9 m 2 + 27 m + 27 Hence, the required answer is m 3 + 9 m 2 + 27 m + 27 .