Question

Factorise 8x8 + 36x²y + 54xy2 + 27y3.​

Answer 1

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• Factorise the given polynomial.

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$8 {x}^{3} + 36 {x}^{2} y + 54x {y}^{2} + 27 {y}^{3}$

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

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

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• ${(2x + 3y)}^{3}$

$\star\:\:\:\bf\large\underline\blue{Identity\:Used:-}$

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