Factorize 8x3 + 27 Y3 + 36x2 Y + 54xy2

Factorize 8x³ + 27 y³ + 36x² y + 54xy²

8x³ + 27 y³ + 36x² y + 54xy²

= (2x)³ + (3y)³ + 3 × (2x)2 × 3y + 3 × (2x)(3y )2

= (2x + 3y )³ [∵ a³ + b³ + 3a²b + 3ab² = (a + b)³]

= (2x + 3y )(2x + 3y )(2x + 3y )

∴ 8x³ + 27 y³ + 36x² y + 54xy² = (2x + 3y )(2x + 3y )(2x + 3y )

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.3 [Page 17]

Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.3 | Q 4 | Page 17

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Match Column I with Column II in the following:

Column I	Column II
1. The difference of 3 and a number squared	(a) 4 – 2x
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6. A number squared plus 6	(f) 2(n + 6)
7. 2 times the sum of a number and 6	(g) 7(n + 1)
8. Three less than the square of a number	(h) n² + 6

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