Question

What is the following product? (4x sqrt5^2 + 2x^2 sqrt6)^2

Answer 1

We expand the perfect square trinomial using the formula: $(a+b)^2=a^2+2ab+b^2$
$(4x^{2} \sqrt{5}+2x^{2} \sqrt{6})^2 \\ =(4x^{2} \sqrt{5})^2 + 2(4x^{2} \sqrt{5})(2x^{2} \sqrt{6})+(2x^{2} \sqrt{6})^2 \\ =80x^4+16x^4 \sqrt{30}+24x^4 \\ =(104+16\sqrt{30})x^4$