Question

Drag the tiles to the correct boxes not all tiles will be used

Answer 1

SOLUTION

We want to determine the right steps that can be used to solve

$\frac{x^2+7x+10}{x^2+4x+4}.\frac{x^2+3x+2}{x^2+6x+5}$

Now the first step will be to factorise each of the quadratic expression This becomes

$\begin{gathered} \frac{x^2+2x+5x+10}{x^2+2x+2x+4}.\frac{x^2+1x+2x+2}{x^2+5x+1x+5} \\ \frac{x(x+2)+5(x+2)}{x(x+2)+2(x+2)}.\frac{x(x+1)+2(x+1)}{x(x+5)+1(x+5)} \\ \frac{(x+2)(x+5)}{(x+2)(x+2)}.\frac{(x+1)(x+2)}{(x+5)(x+1)} \end{gathered}$

Hence the first step to drag into the tile is

$\frac{(x+2)(x+5)}{(x+2)(x+2)}.\frac{(x+1)(x+2)}{(x+5)(x+1)}$

The next step is to cancel out the common factors. This becomes

$\begin{gathered} \frac{(x+2)(x+5)}{(x+2)(x+2)}.\frac{(x+1)(x+2)}{(x+5)(x+1)} \\ \text{Here we cancel out }(x+2)\text{ above and below in the first set and } \\ \text{cancel out }(x+1)\text{ above and below in the second part, we will have} \\ \frac{(x+5)}{(x+2)}.\frac{(x+2)}{(x+5)} \end{gathered}$

Hence, the second step to drag into the tile is

$\frac{(x+5)}{(x+2)}.\frac{(x+2)}{(x+5)}$

The next step is to multiply by bringing them together, and we have

$\begin{gathered} \frac{(x+5)}{(x+2)}.\frac{(x+2)}{(x+5)} \\ =\frac{(x+5)(x+2)}{(x+2)(x+5)} \end{gathered}$

Hence, the third step to drag to the tile is

$\frac{(x+5)(x+2)}{(x+2)(x+5)}$

The next step is to cancel out another common factors if there is

$\begin{gathered} \frac{(x+5)(x+2)}{(x+2)(x+5)} \\ \text{Here, }(x+5)\text{ is se}en\text{ above and below, we will cancel out to have } \\ \frac{(x+2)}{(x+2)} \\ x+2\text{ can cancel out and we will have } \\ 1 \end{gathered}$

Hence, the final step to drag into the tile is 1