Question

10. Factorise each of the following:
(i) 27y3 + 125z
(ii) 64m3 - 343n
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Answer 1

Step-by-step explanation:

I)

$64 {m}^{3} - 343 {n}^{3}$

$first \: we \: use \: {a}^{n} \times {b}^{n} = {ab}^{n}$

${4}^{3} {m}^{3} - {7}^{3} {n}^{3} \\ now \: we \: apply \: the \\ {a}^{n} {b}^{n} = {ab}^{n} \\ ({4m})^{3} - ({7n})^{3} \\ now \: we \: apply \: the \: following \: formula \\ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + {b}^{2} + ab) \\ \\ {4m}^{3} - {7n}^{3} \\ = (4m - 7n)( {4m}^{2} + {7n}^{2} + 28mn)$

ii)