Question

The expansion of ($x-6$)($x+5$)($x-4$) is _____.

• A. $x^3$ + $9$$x^2$ + $26$$x$ + $24$
• B. $x^3$ - $5$$x^2$ - $26$$x$ + $120$
• C. $x^3$ + $18$$x^2$ + $26$$x$ + $24$
• D. $x^3$ + $9$$x^2$ + $26$$x$ + $120$

Answer 1

The correct option is B $x^3$ - $5$$x^2$ - $26$$x$ + $120$

Using the identity,
$(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ca)x+a\times b\times c$,

$(x-6)(x+5)(x-4)$
$=x^3+(-6+5-4)x^2+\left(\right(-6\left)\right(5)+(5\left)\right(-4)+(-4\left)\right(-6\left)\right)x+(-6)\times \left(5\right)\times (-4)$
$=x^3-5x^2-26x+120$.