Question

Simplify: $(6\sqrt{a}-5\sqrt{b})(6\sqrt{a}+5\sqrt{b})$.

Answer 1

The given surds can be simplified as follows:

$(6\sqrt{a}-5\sqrt{b})(6\sqrt{a}+5\sqrt{b})=6\sqrt{a}(6\sqrt{a}+5\sqrt{b})-5\sqrt{b}(6\sqrt{a}+5\sqrt{b})$

$=(6\times 6\sqrt{a\times a})+(6\times 5\sqrt{a\times b})-(5\times 6\sqrt{a\times b})-(5\times 5\sqrt{b\times b})$

$=36a+30\sqrt{ab}-30\sqrt{ab}-25b$

$=36a-25b$ .

Hence, $(6\sqrt{a}-5\sqrt{b})(6\sqrt{a}+5\sqrt{b})=36a-25b$ .