Question

In a expansion of (2x - 3)³, the co-efficient of x is​

Answer 1

Step-by-step explanation:

$\huge{\underline{\underline{Given→}}}$

• $\sf\green{Equation=(2x-3)^3}$

$\huge{\underline{\underline{To\:Find→}}}$

$\sf\pink{→Coefficient\:of\:‘x’\:after\:expanding\:the\:equation.}$

$\huge{\underline{\underline{Answer→}}}$

$({2x - 3})^{3} \\ = ({2x})^{3} + ( { - 3})^{3} + 3(2x)( - 3)(2x - 3) \\ = {8x}^{3} - 27 + - 18x(2x - 3) \\ = {8x}^{3} - 27 - (18x)(2x) - (18x)( - 3) \\ = {8x}^{3} - 27 - {36x}^{2} + 54x \\ = {8x}^{3} - {36x}^{2} + 54x - 27$

$\sf{\boxed{\boxed{\red{→8x^3-36x^2+54x-27✔}}}}$

☞As the x term is +54x so the coefficient of x is 54 which is the required answer.

$\bold{\underline{\underline{Identity\:used→}}}$

$\sf\purple{→(a+b)^3=a^3+b^3+3ab(a+b)}$

HOPE IT HELPS.