Simplify the following expression using the order of operations.
3 left-parenthesis 2 x squared plus 4 right-parenthesis minus 4 left-parenthesis x minus 6 right-parenthesis
(1 point)
Responses
6 x squared minus 4 x plus 36
Image with alt text: 6 x squared minus 4 x plus 36
6 x squared minus 4 x plus 28
Image with alt text: 6 x squared minus 4 x plus 28
2 x squared minus 4 x plus 28
Image with alt text: 2 x squared minus 4 x plus 28
2 x squared plus 4 x plus 28
To simplify the expression, we need to follow the order of operations (also known as PEMDAS).
First, we need to simplify the expressions inside the parentheses.
The expression inside the first set of parentheses is 2x^2 + 4.
The expression inside the second set of parentheses is x - 6.
Now, we can substitute these simplified expressions back into the original expression:
3(2x^2 + 4) - 4(x - 6)
Next, we can distribute the constants to the terms inside the parentheses:
6x^2 + 12 - 4x + 24
Finally, we can combine like terms:
The simplified expression is 6x^2 - 4x + 36.
Therefore, the correct simplification is:
6x^2 - 4x + 36.
To simplify the expression using the order of operations, you need to follow these steps:
1. Start by evaluating the expression inside the parentheses: 2x^2 + 4.
2. Multiply this expression by the number outside the parentheses, which is 3: 3 * (2x^2 + 4) = 6x^2 + 12.
3. Next, evaluate the expression inside the second set of parentheses: x - 6.
4. Multiply this expression by the number outside the parentheses, which is -4: -4 * (x - 6) = -4x + 24.
5. Finally, subtract the second result from the first result: 6x^2 + 12 - (-4x + 24).
Simplifying further, we get: 6x^2 + 12 + 4x - 24.
6. Combine the like terms: 6x^2 + 4x - 12.
Therefore, the simplified expression is 6x^2 + 4x - 12.