Question

factorise 27x3 - 64y3​

Answer 1

Answer:

Factorize 27x3−64y3

ANSWER

27x 3 −64y3

=(3x)3−(4y)3=(3x−4y)[(3x)2+(3x)(4y)+(4y)2]

=(3x+4y)(9x2+12xy+16y 2)

Answer 2

Solution :-

$\bold{ {27x}^{3} - {64y}^{3} }$

$= {3}^{3} {x}^{3} - {4}^{3} {y}^{3}$

$= ( {3x})^{3} - ({4y})^{3}$

$= (3x - 4y)(( {3x})^{2} + 3x \times 4y + ( {4y})^{2} )$

$= (3x - 4y)( {9x}^{2} + 12xy + 16y ^{2} )$

Additional information

• $(x - y) ^{2} = {x}^{2} + {y}^{2} - 2xy$
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• $( x + y) = {x}^{2} + {y}^{2} + 2xy$
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• ${x}^{2} - {y}^{2} = (x + y)(x - y)$
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• $(x + y) ^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$
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• $(x - y) ^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$