Question

Using special products, simplify :

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

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

Step 2: Applying the formula

$$\begin{gathered} (x^2-\frac{2}{7})(x^2+\frac{3}{7})={\left(x^2\right)}^2+(-\frac{2}{7}+\frac{3}{7})x^2+\left[\right(-\frac{2}{7})\times \frac{3}{7}] \\ =x^4+\left(\frac{-2+3}{7}\right)x^2-\frac{6}{49} \\ =x^4+\frac{1}{7}{x}^2-\frac{6}{49} \end{gathered}$$

Hence, the product is $x^4+\frac{1}{7}{x}^2-\frac{6}{49}$.