Question

if a= 3+b, then find the value of a 3 -b 3 -9ab.

Answer 1

Answer:

$\red{Value \: of : a^{3} - b^{3} - 9ab }\green {= 27}$

Step-by-step explanation:

$Given \: a = 3+b$

$\implies a - b = 3\: ---(1)$

/* On cubing both sides of the equation (1),we get

$\implies (a-b)^{3} = 3^{3}$

$\implies a^{3} - b^{3} - 3ab(a-b) = 27$

$\pink ( By \: algebraic\: identity )}$

$\implies a^{3} - b^{3} - 3ab\times 3 = 27$

\* From (1) *\

$\implies a^{3} - b^{3} - 9ab = 27$

Therefore.,

$\red{Value \: of : a^{3} - b^{3} - 9ab }\green {= 27}$

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Answer 2

Answer:

Given a= 3b

so , a-b = 3 = equation 1

On cubing both sides of the equation we get

( a-b) ³ = 3³

a³ - b³ - 3ab ( a-b) = 27 ( Algebraic identify )

a³-b³-9ab = 27

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