Final answer:
To rewrite the expression 3(x+7)3 + 4 x 23 using the distributive property, we expand and cube the terms inside the parentheses and then sum the result with the product of 4 and 23, leading to the simplified expression 27x3 + 64.
Step-by-step explanation:
The distributive property is a useful tool in simplifying algebraic expressions. When we apply the distributive property to a problem like 3(x+7)3 + 4 x 23, we multiply each term inside the parentheses by the number outside before adding the product to the result of the following multiplication.
First, we address the term 3(x+7)3. This is a case of distributing the cube across the addition within the parentheses, then combining it with the multiplication of the 4 x 23. To do this correctly, we need to remember the rule that when we have an expression like (xa)b, it is equivalent to xa.b. Therefore, cubing both terms within the parentheses would give us 33 for the constant and (x3) for the variable, ultimately combining to 27x3.
Next, we consider the 4 x 23. We know that multiplying exponents of the same base can be summarized as xPxQ = x(p+q). Thus, 22 simply becomes 24. Multiplying the result by 4 gives us 4 times 16, which is 64.
Putting it all together, the distributive property applied to the problem simplifies to 27x3 plus 64.