Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Simplify the expression
8²+9(12/3x²)-7.
Explain each

Answer 1

The expression is simplified by first calculating the exponent, then simplifying the multiplication within the parentheses and finally combining like terms. The simplified result is 57 + 36x². Checking the reasonableness of the answer can be done by plugging in a value for x.

Step-by-step explanation:

To simplify the expression 8²+9(12/3x²)-7, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Firstly, let's handle the exponent (8²):

• 8² = 64

Next, we simplify the expression within the parentheses and any multiplication:

• 9(12/3x²)
• First, divide 12 by 3, which gives us 4, so we have:
• 9(4x²)
• Now multiply 9 by 4, which gives us 36, so we have:
• 36x²

Then we incorporate this into the original expression:

• 64 + 36x² - 7

Now, we combine the like terms, which are the constant terms 64 and -7:

• 64 - 7 = 57

Finally, we rewrite the simplified expression:

• 57 + 36x²

To check if our answer is reasonable, we can evaluate it for a specific value of x (e.g., x = 1) and ensure the calculations give a consistent value. If the simplification was done correctly, no matter the value of x, the expression will produce accurate results when evaluated.