Question

Deduce the Algebraic identity for $(x+a)(x+b)(x+c)$ by using the product formula

Answer 1

$(x+a)(x+b)(x+c)$

Using product formula,

$\Rightarrow (x+a)(x+b)(x+c)=(x+a)(x^2+(b+c)x+bc)$

$=x(x^2+(b+c)x+bc)+a(x^2+(b+c)x+bc)$

$=x^3+(b+c)x^2+bcx+a{x}^2+a(b+c)x+ax$

$=x^3+(a+b+c)x^2+(ab+bc+ca)x+ab$

$\Rightarrow (x+a)(x+b)(x+c)=x^3+(a+b+c)x+(ab+bc+ca)x+abc.$

Hence, solved.