Question

Using the Identities, simplify the following

$(x^2+2y^2)(x^2+5y^2)$

Answer 1

Step 1 : We need to identify the identity first, 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 $a=2y^{2}andb=5y^2$

Step 2 : Applying the formula

$$\begin{gathered} (x^2+2y^2)(x^2+5y^2)=x^4+(2y^2+5y^2)x^2+(2y^2\times 5y^2) \\ =x^4+7x^2{y}^2+10y^4 \end{gathered}$$

Hence the solution is $x^4+7x^2{y}^2+10y^4$