Question

using algebraic identity, find the coefficients of x², x and constant term without actual expansion. (2x+3)(2x-5)(2x-6)​

Answer 1

$\huge\mathbb\green{(2x+3)(2x-5)(2x-6)}$

$\huge\mathbb\orange{Co-efficient\:of\:x²=\:4(a+b+c)}$

$\huge\mathbb\red{4(3+(-5)+(-6))}$

$\huge\mathbb\pink{4*(-8)=-32}$

$</p><p>\huge\mathbb\green{Co-efficient\:of\:x=2(ab+bc+ca)}$

$\huge\mathbb\red{2[3×(-5)+(-5)(-6)+(-6)(3)]}$

$\huge\mathbb\orange{2[-15+30-18]=2×(-3)=\:-6}$

$\huge\mathbb\pink{Constants\:terms=\:a\:b\:c}$

$\huge\mathbb\green{3×(-5)×(-6)}$

$\huge\mathbb\red{=\:90}$