How is adding and subtracting
radicals the same as adding and
subtracting polynomials?
It's not, unless you count different roots as being like different variables.
1+2333758=2333759
Adding and subtracting radicals is similar to adding and subtracting polynomials, but there are some key differences. Here are the step-by-step processes for each:
Adding and Subtracting Radicals:
1. Identify radicals that have the same radical expression or index and the same radicand.
2. Add or subtract the coefficients of these radicals, keeping the radical expression and radicand the same.
3. Simplify the resulting expression by combining like terms, if possible.
Note: It is only possible to add or subtract radicals with the same radical expression and radicand.
Adding and Subtracting Polynomials:
1. Identify polynomials that have the same variable(s) and corresponding degrees.
2. Add or subtract the coefficients of like terms. Keep the same variable(s) and degree.
3. Simplify the resulting polynomial by combining like terms, if possible.
Note: Polynomials can have multiple variables and terms with different degrees.
In summary, while the process of combining like terms is similar in adding and subtracting radicals and polynomials, the key difference lies in the presence of a radical expression and radicand in radicals, as opposed to variables and degrees in polynomials.
Adding and subtracting radicals is similar to adding and subtracting polynomials because they both involve combining terms with similar properties. Here's how you can understand the similarity:
To add or subtract radicals, you need to identify the terms with the same radical expression. For example, consider the expression √5 + 2√3 - √5. Here, we have two terms with the same radical √5, which are √5 and -√5.
Similarly, when you add or subtract polynomials, you look for terms with the same variable(s) and raised to the same power(s). For instance, consider the polynomial 3x² + 5x - 2x² - 7x. In this case, we have two terms with the same variable and power, which are 3x² and -2x². We also have two terms with the same variable but different powers, which are 5x and -7x.
When combining like terms, whether it's radicals or polynomials, you add or subtract the coefficients while keeping the same radical or variable part unchanged. In the previous examples:
For the radicals, we have √5 + 2√3 - √5. Since the two √5 terms cancel each other out, we are left with 2√3 as the result.
For the polynomials, we have 3x² + 5x - 2x² - 7x. Combining like terms, we add the coefficients of the terms with the same variables and exponents. Thus, we have 3x² - 2x² + 5x - 7x, which simplifies to x² - 2x.
In both cases, we are essentially grouping similar terms and combining their coefficients. Whether it's radicals with the same root or polynomials with the same variable and power, the process is similar.