Question

Write the following in expanded form: i) (3a-4b)3

ii) (p-
(2÷3)q)3​

Answer 1

Answer:

$(1) \: \: 27 {a}^{3} - 72 {a}^{2} b + 96a {b}^{2} - 64 {b}^{3} \\ \\ (2) \: \: {p}^{3} - \frac{4}{3} {p}^{2} q + \frac{8}{9} p {q}^{2} - \frac{8}{27} {q}^{3}$

Step-by-step explanation:

${(3a - 4b)}^{3} \\ \\ = (3a - 4b)(3a - 4b)(3a - 4b) \\ \\ = (3a - 4b)(9 {a}^{2} - 12ab - 12ab + 16 {b}^{2} ) \\ \\ = (3a - 4b)(9 {a}^{2} - 24ab + 16 {b}^{2} ) \\ \\ = 27 {a}^{3} - 72 {a}^{2} b + 96a {b}^{2} - 64 {b}^{3} \\ \\ \\ \\ {(p - \frac{2}{3}q )}^{3} \\ \\ = (p - \frac{2}{3}q )(p - \frac{2}{3}q )(p - \frac{2}{3}q ) \\ \\ = (p - \frac{2}{3}q )( {p}^{2} - \frac{4}{3} pq + \frac{4}{9} {q}^{2} ) \\ \\ = {p}^{3} - \frac{4}{3} {p}^{2} q + \frac{8}{9} p {q}^{2} - \frac{8}{27} {q}^{3}$

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