Question

Simplify the following using the identities :

$5\left[\right(x^4-\frac{3}{4}\left)\right(x^4+\frac{3}{4}\left)\right]$

Answer 1

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

so if we compare the question with the identity we get $a=x^{4}andb=\frac{3}{4}$

Step 2 : Applying the formula and solving

$$\begin{gathered} 5\left[\right(x^4-\frac{3}{4}\left)\right(x^4+\frac{3}{4}\left)\right]={5\left[\right(x^4)}^2-{\left(\frac{3}{4}\right)}^2] \\ =5[x^8-\frac{9}{16}] \\ =5x^8-\frac{45}{16} \end{gathered}$$

Hence the solution is $5x^8-\frac{45}{16}$