To determine which expression is equivalent to 1 + ³ p − 3 + (−2p), we need to apply the order of operations. The order of operations is a set of rules that specifies the order in which arithmetic operations should be performed in order to get the correct result. The order of operations is often abbreviated using the mnemonic acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
In this case, the first operation that we need to perform is the exponent, which is represented by the symbol ³. This means that we need to calculate ³ p first. Since the cube of a number is the number multiplied by itself three times, we have ³ p = p * p * p = p^3.
Next, we need to perform the multiplication and division operations, which are represented by the symbols * and /, respectively. However, there are no multiplication or division operations in this expression, so we can skip this step.
Finally, we need to perform the addition and subtraction operations, which are represented by the symbols + and -, respectively. In this case, we have the following:
1 + p^3 - 3 + (-2p)
To simplify this expression, we need to perform the addition and subtraction operations from left to right. This means that we need to add 1 and p^3, and then subtract 3 and (-2p) from the result. Since addition and subtraction are performed from left to right, we have the following:
1 + p^3 - 3 + (-2p)
= (1 + p^3) - 3 + (-2p)
= p^3 - 3 + (-2p)
= p^3 - 2p - 3
Therefore, the expression that is equivalent to 1 + ³ p − 3 + (−2p) is p^3 - 2p - 3.