Expand: (i) (3a + 5b)³ (ii) (2p - 3q)³ (iii) (2x + 1/3x)³ (iv) (3ab - 2c)³ (v) (3a - 1/a)³ (vi) ((1/2)x - (2/3)y)³

(i) Given, (3a + 5b)3 Using identity : (a + b)3 = a3 + b3 + 3ab(a + b) ⇒ (3a + 5b)3 = (3a)3 + (5b)3 + 3 × 3a × 5b × (3a + 5b) ⇒ (3a + 5b)3 = 27a3 + 125b3 + 45ab × (3a + 5b) ⇒ (3a + 5b)3 = 27a3 + 135a2 b + 225ab2 + 125b3 Hence, (3a + 5b)3 = 27a3 + 135a2b + 225ab2 + 125b3. (ii) Given, (2p - 3q)3 Using identity : (a - b)3 = a3 - b3 - 3a2b + 3ab2 ⇒ (2p - 3q)3 = [(2p)3 - (3q)3 - 3 × (2p)2 (3q) + 3 × (2p) × (3q)2] ⇒ (2p - 3q)3 = 8p3 - 27q3 - 3 × 4p2 (3q) + 3 × (2p) × 9q2 ⇒ (2p - 3q)3 = 8p3 - 36p2q + 54pq2 - 27q3 Hence, (2p - 3q)3 = 8p3 - 36p2q + 54pq2 - 27q3. (iii) Given, Using identity : (a + b)3 = a3 + b3 + 3a2b + 3ab2 Hence, . (iv) Given, (3ab - 2c)3 Using identity : (a - b)3 = a3 - b3 - 3a2b + 3ab2 ⇒ (3ab - 2c)3 = [(3ab)3 - (2c)3 - 3 × (3ab)2 (2c) + 3 × (3ab) × (2c)2] ⇒ (3ab - 2c)3 = 27a3b3 - 8c3 - (9a2b2) × 6c + 3 × (3ab) × 4c2 ⇒ (3ab - 2c)3 = 27a3b3 - 54a2b2c + 36 abc2 - 8c3 Hence, (3ab - 2c)3 = 27a3b3 - 54a2b2c + 36 abc2 - 8c3. (v) Given, Using identity : (a - b)3 = a3 - b3 - 3a2b + 3ab2 Hence, . (vi) Given, Using identity : (a - b)3 = a3 - b3 - 3a2b + 3ab2 Hence, .

If (a² + b² + c²) = 50 and (ab + bc + ca) = 47, find the value of (a + b + c).

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If (a² + b² + c²) = 89 and (ab - bc - ca) = 16, find the value of (a + b - c).

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Mathematics

Expand: (i) (3a + 5b)³ (ii) (2p - 3q)³ (iii) (2x + 1/3x)³ (iv) (3ab - 2c)³ (v) (3a - 1/a)³ (vi) ((1/2)x - (2/3)y)³

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Related Questions

If (a² + b² + c²) = 50 and (ab + bc + ca) = 47, find the value of (a + b + c).

If (a² + b² + c²) = 89 and (ab - bc - ca) = 16, find the value of (a + b - c).

Mathematics

Expand: (i) (3a + 5b)³ (ii) (2p - 3q)³ (iii) (2x + 1/3x)³ (iv) (3ab - 2c)³ (v) (3a - 1/a)³ (vi) ((1/2)x - (2/3)y)³

Expansions

Related Questions

If (a2 + b2 + c2) = 50 and (ab + bc + ca) = 47, find the value of (a + b + c).

If (a2 + b2 + c2) = 89 and (ab - bc - ca) = 16, find the value of (a + b - c).

If (a² + b² + c²) = 50 and (ab + bc + ca) = 47, find the value of (a + b + c).

If (a² + b² + c²) = 89 and (ab - bc - ca) = 16, find the value of (a + b - c).