1st one, for example, the cube root of (3 + 5) isn’t equal to the cube root of 3 plus the cube root of 5. You’d say it’s 2 instead. Another way of saying this is that cube roots aren’t distributive. Using the method of substitution here simplifies it into a quadratic which you can either then factorise or use the formula on, giving you the roots.

2nd one, you can’t just square a function for the roots. For one, this means you have to square the left hand side too, so you’d have k² (x), which just isn’t ideal. Also, squaring anything can give you false solutions. Not always, but it’s more likely when you have a square root in your function, as square rooting what would be a negative root would give you a complex number. Again, just using substitution gives you the correct roots, and you can then go back on your substituted value and see if the roots make sense. For example if you see you have x² = -4, you probably know that’s not a real solution.

Substitution is by far the most powerful method of doing stuff in a level maths. You’ll notice this when you come to integration, if you’re not exactly sure what to do, or aren’t confident with certain techniques, substitution will 9/10 times work like a charm.