Q:

# How do you simplify polynomials?

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One simplifies polynomial expressions by adding and subtracting like terms. To find like terms, one needs to compare the variable parts of the polynomial's components. It is important to avoid combining mismatched components because doing so produces a new polynomial.

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Terms that have no variable parts can be added together. Terms that have the same variable part can also be combined. Examples of terms with the same variable part are 10z and 3z. However, 6z and 8yz cannot be combined because the second term has an addition variable that the first term lacks. Similarly, 3y and 2y^3 are not like terms because in the first term, the variable has a power of 1, while in the second term it has a power of 3.

An example of a polynomial that can be simplified is 27 + 5x^2 - 6xy + xy + 3x - 9 + 4y + 4x^2. In this example, 5x^2 and 4x^2 are like terms because they both have the variable x to the power of 2. Thus, they can be combined to give 9x^2. The terms 27 and -9 can also be combined because they have no variable part; this gives 18. Finally, 6xy and xy can be combined because they share the same two variables. The terms 3x and 4y cannot be combined with any of the other terms, as none of the other terms has x or y alone as its variable. The simplified polynomial can then be written as 9x^2 - 5xy + 3x + 4y + 18.

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