Question

The expansion of $(x+1)(x+2)(x+3)$ is :

• A. $x^3$ + $6$$x^2$ + $11$$x$ + $6$
• B. $x^3$ + $11$$x^2$ + $11$$x$ + $6$
• C. $x^3$ + $6$$x^2$ + $11$$x$ + $6$
• D. $x^3$ + $6$$x^2$ - $11$$x$ + $6$

Answer 1

The correct option is A $x^3$ + $6$$x^2$ + $11$$x$ + $6$

Using the identity
$(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ca)x+a\times b\times c$,
$(x+1)(x+2)(x+3)=x^3+(1+2+3)x^2+\left(\right(1\left)\right(2)+(2\left)\right(3)+(3\left)\right(1)x+1\times 2\times 3$
$=x^3+6x^2+11x+6$.