If a + 2b = 5, prove that a 3 + 8b 3 + 30ab = 125.

We know that, ⇒ (a + 2b) 3 = a 3 + 8b 3 + 3(a)(2b)(a + 2b) Substituting values in above formula, ⇒ 5 3 = a 3 + 8b 3 + 6ab × 5 ⇒ 125 = a 3 + 8b 3 + 30ab. Hence, proved that a 3 + 8b 3 + 30ab = 125.

Mathematics

If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.

Expansions

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Answer

We know that,

⇒ (a + 2b)³ = a³ + 8b³ + 3(a)(2b)(a + 2b)

Substituting values in above formula,

⇒ 5³ = a³ + 8b³ + 6ab × 5
⇒ 125 = a³ + 8b³ + 30ab.

Hence, proved that a³ + 8b³ + 30ab = 125.

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Mathematics

If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.

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Answer

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If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.