Question

The expansion of ($x+2$)($x+3$)($x+4$) is ______.

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

Answer 1

The correct option is A $x^3$ + $9$$x^2$ + $26$$x$ + $24$

Using the identity

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

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

= $x^3$ + $9$$x^2$ + $26$$x$ + $24$.