Write the following form in expanded form:-
(A) ${(2 a + 3 b)}^{3}$
(B) ${(5 x - 3 y)}^{3}$

Open in App

Solution

(A) $= (2 a + 3 b)^{3}$
$=$ $C_{0}^{3} {(2 a)}^{3} + C_{1}^{3} {(2 a)}^{2} {(3 b)}^{1} + C_{2}^{3} {(2 a)}^{1} {(3 b)}^{2} + C_{3}^{3} {(3 b)}^{3}$
$=$ ${(2 a)}^{3} + 3 {(2 a)}^{2} {(3 b)}^{1} + 3 {(2 a)}^{1} {(3 b)}^{2} + {(3 b)}^{3}$
$=$ ${8 a}^{3} + 36 a^{2} b + 54 a b^{2} + 27 b^{3}$
(B) $= (5 x - 3 y)^{3}$
$=$ $C_{0}^{3} {(5 x)}^{3} + C_{1}^{3} {(5 x)}^{2} {(- 3 y)}^{1} + C_{2}^{3} {(5 x)}^{1} {(- 3 y)}^{2} + C_{3}^{3} {(- 3 y)}^{3}$
$=$ ${(5 x)}^{3} + 3 {(5 x)}^{2} {(- 3 y)}^{1} + 3 {(5 x)}^{1} {(- 3 y)}^{2} + {(- 3 y)}^{3}$
$=$ ${125 x}^{3} - 225 x^{2} y + 135 x y^{2} - 27 y^{3}$

Suggest Corrections

Similar questions

(2 a + 3 b)^{3}

Write the following cubes in expanded form: ${(2 a - 3 b)}^{3}$

(2 a + 3 b)^{3}

(5 x - 3 y)^{3}

Write the following cubes in expanded form:
(i) ${(2 x + 1)}^{3}$
(ii) ${(2 a - 3 b)}^{3}$

Join BYJU'S Learning Program