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Question

Factorise :
8x3+27y3+125z3−90xyz

A
(x3y+5z)(4x2+y2+25z2+6xy15yz10xz)
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B
(2x+3y+5z)(4x2+9y2+5z2+6xyyz10xz)
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C
(2x+3y+5z)(4x2+9y2+25z2+6xy15yz10xz)
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D
(x+y5z)(4x2+9y2+25z2+xy15yz10xz)
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Solution

The correct option is C (2x+3y+5z)(4x2+9y2+25z2+6xy15yz10xz)
8x3+27y3+125z390xyz
Using,
a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)
Here,
a=2x
b=3y
c=5z,
Therefore,
=>(2x)3+(3y)3+(5z)33×2x×3y×5z=(2x+3y+5z)(4x2+9y2+25z2+6xy15yz10xz)

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