Question

Factorise 27p*p*p -64Q*Q*Q

Answer 1

Step-by-step explanation:

27p×p×p-64q×q×q

9×3×p×p×p-8×8×q×q×q

p(9×3×p×p)-8q(8×q×q)

Answer 2

Correct Question:-

Factorise

125p³ - 64q³

Solution:-

➡️Write (125p³ - 64q³) in the form of (a3 - b3).

125p³ - 64q³  =  (5p)³ - (4q)³

➡️(5p)³ - (4q)³ is in the form of (a³ - b³).

➡️Comparing (a³ - b³) and (5p)³ - (4q)³, we get

a  =  5p

b  =  4q

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

a³ - b³  =  (a - b)(a² + ab + b²)

➡️Substitute 5p for a and 4q for b. 

(5p)³ - (4q)³  =  (5p - 4q)[(5p)² + (5p)(4q) + (4q)²]

125p³ - 64q³  =  (5p - 4q)(25p² + 20pq + 16q²)

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)