Question

The expansion of ($x-1$)($x-3$)($x+4$) is _______.

• A. $x^3$- $13$$x$ + $24$
• B. $x^3$- $13$$x$ + $12$
• C. $x^3$ + $9$$x^2$ - $13$$x$ + $12$
• D. $x^3$ + $9$$x^2$ + $26$$x$ + $24$

Answer 1

The correct option is B $x^3$- $13$$x$ + $12$

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)$$(x-3)$$(x+4)$

= $x^3$ +$(-1-3+4)$$x^2$ + $\left(\right(-1\left)\right(-3)+(-3\left)\right(4)+(4\left)\right(-1\left)\right)$$x$ + $(-1)\times (-3)\times \left(4\right)$

= $x^3$- $13$$x$ + $12$.