Question

I have a question that came up on my homework. 5^1 + 10^1= 15^1

but

5^2 + 10^2 ≠ 15^2

How are these not equal?

Answer 1

5^2 = 25, 10^2 = 100, so the anser to the left side is 125 15^2 is 225

Answer 2

In general

a^2 + b^2 is not equal to (a+b)^2. There may be the odd example where it’s true but it’s not generalizable to all numbers.

Remember order of operations. Squaring a and b and then adding the result vs. adding them and then squaring the result is not the same set of operations the exponent is always applied before adding.

Answer 3

Thanks!

Answer 4

The reason why 10^1 + 5^1 = 15^1 works is because you’re only raising each number to the power of 1 so you’re not changing the value of 10, 5, or 15, so it’s a matter of 10 + 5 = 15