Write the following in expanded form: 2 x + 3 3

Use identity ( a + b ) 3 = a 3 + b 3 + 3 a b ( a + b ) Consider, a = 2 x and b = 3 Hence, we have, 2 x + 3 3 = 2 x 3 + 3 3 + 3 2 x 3 2 x + 3 = 2 2 x 3 + 27 + 18 x 2 + 27 2 x = 2 2 x 3 + 18 x 2 + 27 2 x + 27 Therefore, the required answer is 2 2 x 3 + 18 x 2 + 27 2 x + 27 .

Write the following in expanded form: 3 + 4 y 3

Use identity ( a + b ) 3 = a 3 + b 3 + 3 a b ( a + b ) Consider, a = 3 and b = 4 y Hence, we have, 3 + 4 y 3 = 3 3 + 4 y 3 + 3 3 4 y 3 - 4 y = ( 3 ) 3 + ( 4 y ) 3 + 12 3 y ( 3 - 4 y ) = 3 3 + 64 y 3 + 36 y + 48 3 y 2 = 3 3 + 36 y + 48 3 y 2 + 64 y 3 Therefore, the required answer is 3 3 + 36 y + 48 3 y 2 + 64 y 3 .

Write the following in expanded form: 1 - 2 y 3

Use identity ( a - b ) 3 = a 3 - b 3 - 3 a b ( a - b ) Consider, a = 1 and b = 2 y Hence, we have, 1 - 2 y 3 = 1 3 - 2 y 3 - 3 1 2 y 1 - 2 y = 1 - 2 2 y 3 - 3 2 y + 6 y 2 = 1 - 3 2 y + 6 y 2 - 2 2 y 3 Therefore, the required answer is 1 - 3 2 y + 6 y 2 - 2 2 y 3 .