If 4a + 3b = 10 and ab = 2, find the value of (64 a³ + 27 b³)

Given, (4a + 3b) = 10 ab = 2 ⇒ (4a + 3b)3 = [(4a)3 + (3b)3 + 3 × 4a × 3b × (4a + 3b)] ⇒ (10)3 = 64a3 + 27b3 + 36ab × (10) ⇒ 1000 = 64a3 + 27b3 + 36 × 2 × 10 ⇒ 1000 = 64a3 + 27b3 + 720 ⇒ 64a3 + 27b3 = 1000 - 720 ⇒ 64a3 + 27b3 = 280 Hence, 64a3 + 27b3 = 280.

Mathematics

If 4a + 3b = 10 and ab = 2, find the value of $64a^3 + 27b^3$ .

Expansions

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Answer

Given,

(4a + 3b) = 10

ab = 2

⇒ (4a + 3b)³ = [(4a)³ + (3b)³ + 3 × 4a × 3b × (4a + 3b)]

⇒ (10)³ = 64a³ + 27b³ + 36ab × (10)

⇒ 1000 = 64a³ + 27b³ + 36 × 2 × 10

⇒ 1000 = 64a³ + 27b³ + 720

⇒ 64a³ + 27b³ = 1000 - 720

⇒ 64a³ + 27b³ = 280

Hence, 64a³ + 27b³ = 280.

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Mathematics

If 4a + 3b = 10 and ab = 2, find the value of $64a^3 + 27b^3$ .

Expansions

Answer

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If 4a + 3b = 10 and ab = 2, find the value of $64a^3 + 27b^3$ .

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

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(ii) (2p - 3q)³
(iii) $\Big(2x + \dfrac{1}{3x}\Big)^3$
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(v) $\Big(3a - \dfrac{1}{a}\Big)^3$
(vi) $\Big(\dfrac{1}{2}x - \dfrac{2}{3}y\Big)^3$

If 3x – 2y = 5 and xy = 6, find the value of $27x^3 - 8y^3$ .

If a + 3b = 6, show that $a^3 + 27b^3 + 54ab = 216$ .