Question

Using special products, simplify :

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

Answer 1

Step 1: Identification of identity

We need to identify the identity first,

Here, the question is in the form of $(x-a)(x+a)$ which is equal to $x^2-a^2$.

So if we compare the question with the identity we get $x=x^2,a=\frac{3}{2}$

Step 2 : Applying the formula and solving

$$\begin{gathered} (x^2-\frac{3}{2})(x^2+\frac{3}{2})={\left(x^2\right)}^2-{\left(\frac{3}{2}\right)}^2 \\ =x^4-\frac{9}{4} \end{gathered}$$

Hence, the product is $x^4-\frac{9}{4}$.