Question

Using the Identities, simplify the following

$(x-5)(x-2)$

Answer 1

Step 1 : We need to identify the identity first, the question is in the form of $(x+a)(x+b)$ which is equal to $x^2+(a+b)x+ab$

so if we compare the question with the identity we get $a=-5andb=-2$

Step 2 : Applying the formula

$$\begin{gathered} (x-5)(x-2)=x^2+(-5-2)x+\left[\right(-5)\times (-2\left)\right] \\ =x^2-7x+10 \end{gathered}$$

Hence the solution is $x^2-7x+10$