Question

(i) (1/2 * a - 3b)(3b + 1/2 * a) * (1/4 * a ^ 2 + 9b ^ 2)

Simplify the sum please fast​

Answer 1

Answer:

$( \frac{1}{2} a - 3b)(3b + \frac{1}{2} a)( \frac{1}{4} {a}^{2} + 9 {b}^{2} ) \\ = ( \frac{1}{2} a - 3b)( \frac{1}{2} a + 3b)( \frac{1}{4} {a}^{2} + 9 {b}^{2} ) \\ using \: the \: formula: (a-b)(a+b) = a²- b²\\ = (( { \frac{1}{2} a})^{2} - ({3b})^{2})(\frac{1}{4} {a}^{2} + 9 {b}^{2} ) \\ = (\frac{1}{4} {a}^{2} - 9 {b}^{2} )(\frac{1}{4} {a}^{2} + 9 {b}^{2} ) \\ again \: using \: same \: formula, \\ = ( { \frac{1}{4} {a}^{2} })^{2} - {(9 {b}^{2} })^{2} \\ = \frac{1}{16} {a}^{4} - 81 {b}^{4}$