Lösning 2.1:2a

First, multiply the brackets together. In the first product, every term in the first bracket is multiplied by every term in the second bracket,

\displaystyle \qquad \begin{align} (x-4)(x-5)-3x(2x-3)&= x\cdot x-x\cdot 5- 4\cdot x-4\cdot (-5)-(3x \cdot 2x-3x\cdot 3)\\ &= x^2-5x-4x+20-(6x^2-9x)\\ &=x^2-5x-4x+20-6x^2+9x \end{align}

Then, gather together \displaystyle x^2-, \, x- and the constant terms and simplify

\displaystyle \qquad \begin{align} \phantom{(x-4)(x-5)-3x(2x-3)}&= (x^2-6x^2)+(-5x-4x+9x)+20 \\ &= -5x^2+0+20\\ &= -5x^2+20 \end{align}