Question

In the expansion (x - 5)³ the coefficient of x² is ..​

Answer 1

Answer:

(x-5)³= x³-3*x²*5+3*x*5²-5³

=x³-15x²+75x-125

that of coefficient of x² is -15

Answer 2

Step-by-step explanation:

$\huge\red{\underline{\underline{\bf Question:-}}}$

In the expansion (x - 5)³ the coefficient of x² is ?

$\\ \\ \huge\red{\underline{\underline{\bf Answer:-}}}$

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

${(x - 5)}^{3} = (x - 5)( {x}^{2} + 25 - 10x) \\ \\{(x-5) }^{3} = {x}^{3} +25x - 10{x}^{2} - 5{x}^{2} - 125 - 50x\\ \\{(x-5) }^{3} = {x}^{3} - 15{x}^{2} - 25 x - 125$

$So, \: coefficient \: of \: {x}^{2} \: is \: \huge\red{ 15 }$