Is adding polynomials and combining radicals through addition and subtraction the same?
The addition and subtraction of polynomials follows the same path the polynomials do.
Hence, if you need to combine radicals, you need to test if they are like radicals, thus, you need to check if they have equal radicands and equal orders.
Hence, when you perform the addition or subtraction of like radicals, you just need to add or subtract its coefficients, the same way you do when you perform the addition or subtraction of polynomials.
You can better understand considering the following simple example that contains an addition of two like radicals, such that:
`4sqrt a + 5sqrt a = (4+5)sqrt a = 9sqrt a`
If the form of radical is more complicated, you need to perform a simplification first and then you may compare if the radicals involved in addition or subtraction are like radicals.
You can better understand considering the following example that contains an addition of two like radicals, such that:
`2sqrt(2x^3) + 5sqrt(8x^3)`
You need to perform the simplification of radicals such that:
`2sqrt(2x^3) + 5sqrt(8x^3) = 2xsqrt(2x) + 5*2xsqrt(2x)`
Now the radicals contain the same radicand and they have the same order, thus, you may perform the addition, such that:
`2xsqrt(2x) + 5*2xsqrt(2x) = 12xsqrt(2x)`
Hence, as a conclusion, either you add or subtract polynomials, or combine like radicals, the method of reasoning is similar, both cases.