Question

Factors of 8x3 + 27y3 are .

Answer 1

Answer:

Hello friend here is your answer.

Step-by-step explanation:

Factors are (2x and 3 y) okay

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Answer 2

SOLUTION:-

Write (8x³- 27y³) in the form of (a³ - b³).

8x³ - 27y³ =  (2x)³ - (3y)³

(2x)³ - (3y)³ is in the form of (a³ - b³).

Comparing (a³ - b³) and (2x)³ - (3y)³, we get

a  =  2x

b  =  3y

Write the formula for (a³ - b³) given in case 2 above.

a³ - b³  =  (a - b)(a²+ ab + b²)

Substitute 2x for a and 3y for b. 

(2x)³ - (3y)³ =  (2x - 3y)[(2x)² + (2x)(3y) + (3y)²]

8x³ - 27y³  =  (2x - 3y)(4x² + 6xy + 9y²)

General step for Factorising

•a³ - b³  =  (a - b)³ + 3ab(a - b)

•a³ - b³  =  (a - b)[(a - b)² + 3ab]

•a³ - b³  =  (a - b)[a² - 2ab + b² + 3ab]

•a³ - b³  =  (a - b)(a² + ab + b²)