Verify: (p - q) (p² + pq + q²) = p³ - q³

Solution:

Given, (p - q) (p² + pq + q²) = p³ - q³

L.H.S = (p - q) (p² + pq + q²)

= p³ + p²q + pq² - qp² - pq² - q³

= p³ - q³

= R.H.S

✦ Try This: Verify: (p - q) (p² + pq + q²) = p³ - q³ if p = 3 and q = 8

Given, (p - q) (p² + pq + q²) = p³ - q³ and p = 3 and q = 8

Substituting the values of p and q,

L.H.S = (p - q) (p² + pq + q²)

= (3 - 8) (3² + (3)(8) + 8²)

= -5(97) = -485

R.H.S = p³ - q³

= (3)³ - (8)³

= 27 - 512 = -485

L.H.S. = R.H.S.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 113(iii)

Verify: (p - q) (p² + pq + q²) = p³ - q³

Summary:

(p - q) (p² + pq + q²) = p³ - q³ is true

☛ Related Questions:

• Verify: (m + n) (m² - mn + n²) = m³ + n³
• Verify: (a + b) (a + b) (a + b) = a³ + 3a²b + 3ab² + b³
• Verify: (a - b) (a - b) (a - b) = a³ - 3a²b + 3ab² - b³