Q) If a + 2b = 5, prove that a3+8b3+30ab=125 - Maths - Expansions

Question

Q) If a + 2b = 5, prove that a 3 + 8 b 3 + 30 a b = 125

Sandeep Saurav · Accepted Answer

Dear Student,

Given : a+2b=5To prove : a3+8b3+30ab=125proof : a+2b=5cubing both the sides⇒(a+2b)3=53⇒a3+(2b)3+3(a)(2b)(a+2b)=125⇒a3+8b3+6ab(a+2b)=125⇒a3+8b3+6ab×5=125 (since a+2b=5)⇒a3+8b3+30ab=125proved
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Q). If a + 2b = 5, prove that a 3 + 8 b 3 + 30 a b = 125 .

Q). If a + 2b = 5, prove that $a^{3} + 8 b^{3} + 30 a b = 125$ .