Question

Use suitable identity to solve $\left(y^2-\frac{3}{2}\right)\left(y^2+\frac{3}{2}\right)$

Answer 1

Finding $\left(y^2-\frac{3}{2}\right)\left(y^2+\frac{3}{2}\right)$:

Using the identity,

$\left(a-b\right)\left(a+b\right)=a^2-b^2$,

On comparing, $\left(y^2-\frac{3}{2}\right)\left(y^2+\frac{3}{2}\right)$ with $\left(a-b\right)\left(a+b\right)$, we get,

$a=y^2,b=\frac{3}{2}$,

$\begin{array}{rcl}\therefore \left(y^2-\frac{3}{2}\right)\left(y^2+\frac{3}{2}\right)& =& {\left(y^2\right)}^2-{\left(\frac{3}{2}\right)}^2\\ & =& \left(y^2\times y^2\right)-\left(\frac{3}{2}\times \frac{3}{2}\right)\\ & =& y^4-\frac{9}{4}\end{array}$

Hence, the required solution is $y^4-\frac{9}{4}$