Question

The expansion of $(x-2)(x+5)(x+7)$ is :

• A. $x^3$+ $10$$x^2$ + $11$$x$ - $70$
• B. $x^3$- $10$$x^2$ + $11$$x$ - $70$
• C. $x^3$+ $10$$x^2$ - $11$$x$ - $70$
• D. $x^3$+ $10$$x^2$ + $11$$x$ + $70$

Answer 1

The correct option is A $x^3$+ $10$$x^2$ + $11$$x$ - $70$

Using the identity
$(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ca)x+a\times b\times c$,
$(x-2)(x+5)(x+7)=x^3+(-2+5+7)x^2+\left(\right(-2\left)\right(5)+(5\left)\right(7)+(7\left)\right(-2\left)\right)x+(-2)\times \left(5\right)\times \left(7\right)$
$=x^3+10x^2+11x-70$.