Question

write the following cube in expanded form
a} [3a+4b]^3 b} [5p-3q]^3

Answer 1

a)

${(3a +4b)}^{3} = {(3a)}^{3} + {(4b)}^{3} + 3(3a)(4b)(3a + 4b) \\ = 27 {a}^{3} + 64 {b}^{3} + 36ab(3a + 4b) \\ = 27 {a}^{3} + 64 {b}^{3} + 108 {a}^{2}b + 144a {b}^{2}$

b)

${(5p - 3q)}^{3} = {(5p)}^{3} - {(3q)}^{3} + 3(5p)(3q)(5p - 3q) \\ = 125 {p}^{3} - 27 {q}^{3} + 45pq(5p - 3q) \\ = 125 {p}^{3} - 27 {q}^{3} + 225 {p}^{2}q - 135p {q}^{2}$

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