Question

(1+3√2)(1-3√2) (3-5√3)(3+5√3)

Answer 1

$1)(1+3\sqrt{2})(1-3\sqrt{2}) =1^{2}-(3\sqrt{2} )^{2}=1-18=\boxed{-17}\\\\\\2)(3-5\sqrt{3})(3+5\sqrt{3})=3^{2} -(5\sqrt{3})^{2}=9-75=\boxed{-66}$

Answer 2

To simplify these expressions, you can use the difference of squares formula:

For any numbers "a" and "b," (a + b)(a - b) = a^2 - b^2.

Let's apply this formula to your expressions:

1. (1 + 3√2)(1 - 3√2): Using the difference of squares formula, we have: (1 + 3√2)(1 - 3√2) = 1^2 - (3√2)^2 = 1 - 18 = -17.

2. (3 - 5√3)(3 + 5√3): Again, using the difference of squares formula: (3 - 5√3)(3 + 5√3) = 3^2 - (5√3)^2 = 9 - 75 = -66.

So, the simplified results are:

1. (1 + 3√2)(1 - 3√2) = -17.
2. (3 - 5√3)(3 + 5√3) = -66.