Question

Using special products, simplify :

$(x+\frac{7}{2})(x-\frac{3}{2})$

Answer 1

Step 1: Identification of identity

We need to identify the identity first,

Here ,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 $a=\frac{7}{2},b=-\frac{3}{2}$

Step 2 : Applying the formula

$$\begin{gathered} (x+\frac{7}{2})(x-\frac{3}{2})=x^2+(\frac{7}{2}-\frac{3}{2})x+[\frac{7}{2}\times (-\frac{3}{2}\left)\right] \\ =x^2+\left(\frac{7-3}{2}\right)x-\frac{21}{4} \\ =x^2+\frac{4}{2}x-\frac{21}{4} \\ =x^2+2x-\frac{21}{4} \end{gathered}$$

Hence, the product is $x^2+2x-\frac{21}{4}$.