Prove the following

(i) $x^{2}+9 x+18=x^{2}+6 x+3 x+18$    [by splitting middle term]

$=x(x+6)+3(x+6)=(x+3)(x+6)$

(ii) $6 x^{2}+7 x-3=6 x^{2}+9 x-2 x-3$    [by splitting middle term]

$=3 x(2 x+3)-1(2 x+3)=(3 x-1)(2 x+3)$

(iii) $2 x^{2}-7 x-15=2 x^{2}-10 x+3 x-15$ [by splitting middle term]

$=2 x(x-5)+3(x-5)=(2 x+3)(x-5)$

(iv) $84-2 r-2 r^{2}=-2\left(r^{2}+r-42\right)$

$=-2\left(r^{2}+7 r-6 r-42\right)$

$=-2[r(r+7)-6(r+7)]$

$=-2(r-6)(r+7)=2(6-r)(r+7)$