Question

Evaluate the product of $(\sqrt{7}x+\sqrt{5})(\sqrt{5}x+\sqrt{7})$

Answer 1

The given polynomials are $\sqrt{7}x+\sqrt{5}$ and $\sqrt{5}x+\sqrt{7}$ we multiply them as follows:

$(\sqrt{7}x+\sqrt{5})(\sqrt{5}x+\sqrt{7})=(\sqrt{7}x\times \sqrt{5}x)+(\sqrt{7}x\times \sqrt{7})+(\sqrt{5}\times \sqrt{5}x)+(\sqrt{5}\times \sqrt{7})=\sqrt{35}{x}^2+7x+5x+\sqrt{35}$

$=\sqrt{35}{x}^2+12x+\sqrt{35}$

Hence, $(\sqrt{7}x+\sqrt{5})(\sqrt{5}x+\sqrt{7})=\sqrt{35}{x}^2+12x+\sqrt{35}$.