Question

Find the coefficient of y in the expansion of (2y-3) Ka whole cube

Answer 1

$Expansion \: of \: (2y-3)^{3} \\= (2y)^{3} - 3\times (2y)^{2} \times 3 + 3 \times (2y)\times 3^{2} - 3^{3}$

$\underline { \blue { By \: Algebraic \: Identity :}}$

$\boxed {\pink { (a-b)^{3} = a^{3}-3a^{2}b+3ab^{2}-b^{3}}}$

$= 8y^{3} - 3 \times 4y^{2} \times 3 + 3 \times 2y \times 9 - 27 \\= 8y^{3} - 36y^{2} + \pink {54}y - 27$

$Now,\red { Coefficient \: of \: y } = 54$

Therefore.,

$\red { Coefficient \: of \: y } \green {= 54}$

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