Generate six Pythagorean triples using any method discussed during class. Explain each method you use.

Answer:1) (3,4,5)2) (6,8,10)3) (8,15,17)4) (10,24,26)5) (5,12,13)6) (33,56,65)Step-by-step explanation:There are many ways of generating Pythagorean triples (a,b,c), one of the easiest ones is to take two natural numbers n and m, and we will have:a = n² - m²,b = 2nm, c = n² + m²Then (a, b, c) is a Pythagorean triple.So, we're going to generate 6 Pythagorean triples using this method.1. m= 1 and n = 2 ⇒a = 2² - 1² = 3b =2(1)(2) = 4c= 1² + 2² = 5and the triple is (3,4,5)2. Now for m = 1 and n = 3⇒a = 3²-1² = 8b= 2(3)(1) =6c = 1²+3² = 10and the triple is (6,8,10)3. Now for m = 1 and n = 4⇒a = 4²-1²=15b=2(1)(4)=8c= 4²+1²=17And the triple is (8,15,17)4. Now for m = 1 and n =5⇒a = 5²-1²=24b=2(1)(5)=10c= 5²+1²=26and the triple is (10,24,26)5. m = 2 n = 3⇒a = 3²-2²= 5b= 2(2)(3)=12c= 3²+2²= 13And the triple is (5,12,13)6. m= 4 n = 7⇒a= 7²-4²=33b=2(7)(4)=56c= 4²+7²= 65And the triple is (33,56,65)