Find the product of ((2/3)x^2 + 5y^2) ((2/3)x^2 + 5y^2)

Question

Find the product of (\(\frac{2}{3}\)x² + 5y²) (\(\frac{2}{3}\)x² + 5y²)

Answer 1

(\(\frac{2}{3}\)x² + 5y²) (\(\frac{2}{3}\)x² + 5y²) = (\(\frac{2}{3}\)x² + 5y²)²

We have (a + b)² = a² + 2ab + b²

Here a = \(\frac{2}{3}\)x² 

b = 5y²

(23 x² + 5y²)² = (23 x²)² + 2 x 23 x² (x) 5y² + (5y²)²

= (\(\frac{2}{3}\))² (x²)² + \(\frac{20x^2y^2}{3}\) + 52(y²)²

(\(\frac{2}{3}\)x² + 5y²)² = \(\frac{4}{9}\)x⁴ + \(\frac{20x^2y^2}{3}\) + 25y⁴