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Factorise each of the following: (i) 27y^3+125z^3 (ii) 64m^3-3

Question

Factorise each of the following:
(i) $27 y^{3} + 125 z^{3}$
(ii) $64 m^{3} - 343 n^{3}$

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Theodore Discussed

Factorise each of the following:
(i)

27 y^{3} + 125 z^{3}

(ii)

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

15 mins ago

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15 mins ago

Text solutionVerified

(i)

27 y^{3} + 125 z^{3} = (3 y)^{3} + (5 z)^{3} = (3 y + 5 z) {(3 y)^{2} - (3 y) (5 z) + (5 z)^{2}}

= (3 y + 5 z) (9 y^{2} - 15 yz + 25 z^{2})

(ii)

64 m^{3} - 343 n^{3} = (4 m)^{3} - (7 n)^{3} = (4 m - 7 n) {(4 m)^{2} + (4 m) (7 n) + (7 n)^{2}}

= (4 m - 7 n) (16 m^{2} + 28 mn + 49 n^{2})

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Question Text	Factorise each of the following: (i) $27 y^{3} + 125 z^{3}$ (ii) $64 m^{3} - 343 n^{3}$
Answer Type	Text solution:1
Upvotes	150