Question

Simplify a(cube)-1000b(cube) 64a(cube)-125b(cube)

Answer 1

The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.

Simplification

Question 1: a³ - 1000b³

a³ - b³

= (a-b) × (a² +ab +b²)

• 1000 is the cube of 10
• a³ is the cube of a¹
• b³ is the cube of b¹

So,

(a - 10b) × (a² + 10ab + 100b²)

Question 2: 64a³ - 125b³

a³ - b³

= (a-b) × (a² +ab +b²)

• 64 is the cube of 4
• 125 is the cube of 5
• a³ is the cube of a¹
• b³ is the cube of b¹

So,

(4a - 5b) • (16a² + 20ab + 25b²)

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