Answer
$\textbf{(a)}\hspace{0.7cm} 11x-2$
$\textbf{(b)}\hspace{0.7cm} 4x^2+7x-15$
$\textbf{(c)}\hspace{0.7cm} a-b$
$\textbf{(d)}\hspace{0.7cm} 4x^2+12x+9$
$\textbf{(e)}\hspace{0.7cm} x^3+6x^2+12x+8$
$\textbf{(f)}\hspace{0.7cm} x^4+9x^2$
Work Step by Step
$\textbf{(a)}\hspace{0.7cm} 3(x+6)+4(2x-5)=(3x+18)+(8x-20)=11x-2$
$\textbf{(b)}\hspace{0.7cm} (x+3)(4x-5)=x(4x-5)+3(4x-5)=4x^2-5x+12x-15=4x^2+7x-15$
$\textbf{(c)}\hspace{0.7cm} (\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})=\sqrt{a}(\sqrt{a}-\sqrt{b})+\sqrt{b}(\sqrt{a}-\sqrt{b})=a-\sqrt{a}\sqrt{b}+\sqrt{b}\sqrt{a}-b=a-b$
$\textbf{(d)}\hspace{0.7cm} (2x+3)^2=(2x+3)(2x+3)=2x(2x+3)+3(2x+3)=4x^2+12x+9$
$\textbf{(e)}\hspace{0.7cm} (x+2)^3=(x+2)(x+2)(x+2)=(x+2)(x^2+2x+2x+4)=(x+2)(x^2+4x+4)=x(x^2+4x+4)+2(x^2+4x+4)=x^3+4x^2+4x+2x^2+8x+8=x^3+6x^2+12x+8$
$\textbf{(f)}\hspace{0.7cm} x^2(x-3)(x+3)=x^2(x(x+3)-3(x+3))=x^2(x^2+3x-3x+9)=x^2(x^2+9)=x^4+9x^2$