Verify: (ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab) = 0

Solution:

Given, (ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab) = 0

Here, L.H.S = (ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab)

Using standard identity: a² - b² = (a + b) (a - b),

L.H.S= [(ab)² - (bc)²] + [(bc)² - (ca)²] + [(ca)² - (ab)²]

= (ab)² - (bc)² + (bc)² - (ca)² + (ca)² - (ab)²

= (ab)² - (ab)² - (bc)² + (bc)² - (ca)² + (ca)²

= 0

= R.H.S

✦ Try This: Verify that, (am + bn)(am - bn) +(bm + cn)(bm - cn) + (cm + an)(cm - an) = 0

Given, (am + bn)(am - bn) +(bm + cn)(bm - cn) + (cm + an)(cm - an) = 0

L.H.S = (am + bn)(am - bn) +(bm + cn)(bm - cn) + (cm + an)(cm - an)

= [(am)² - (bn)²] + [(bm)² - (cn)²] + [(cm)² - (an)²]

≠ 0

∴ 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(i)

Verify: (ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab) = 0

Summary:

(ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab) = 0 is true

☛ Related Questions:

• Verify: (a + b + c) (a² + b² + c² - ab - bc - ca) = a³ + b³+ c³ - 3abc
• Verify: (p - q) (p² + pq + q²) = p³ - q³
• Verify: (m + n) (m² - mn + n²) = m³ + n³