Question

Factories 8x³+27y³+36x²y+54xy²​

Answer 1

Step-by-step explanation:

METHOD 1 :

2x + 3y = 13 ……….(1)

Cubing both sides :

(2x + 3y)³ = 2197

Using (a + b)³ = a³ + b³ + 3 ab (a + b) ,

= > 8x³ + 27y³ + 3 × 2 x × 3 y (2 x + 3 y ) = 2197

From (1) we have :

= > 8x³ + 27y³ + 18 xy(13) = 2197

= > 8x³ + 27y³ + 18×6×13 = 2197

= > 8x³ + 27y³ + 1404 = 2197

= > 8x³ + 27y³ = 2197 - 1404

= > 8x³ + 27y³ = 793

METHOD 2 :

2x + 3y - 13 = 0

If a + b + c = 0 , a³ + b³ + c³ = 3 abc

= > 8x³ + 27y³ - 2197 = 3 × (-13) × 6 xy

= > 8x³ + 27y³ - 2197 = - 234 × 6

= > 8x³ + 27y³ = 2197 - 1404

= > 8x³ + 27y³ = 793

Answer 2

Explanation:

$8x^3 + 27y^3 + 36x^2y + 54xy^2$

$=(2x)^3+(3y)^3+18xy(2x+3y)$

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

$=(2x+3y)^3$ [because $(a+b)^3 = a^3 + b^3 + 3ab(a+b)$]

Answer: (2x+3y)^3