Final answer:
By using the distributive property, the expression 4(2x + 11 - 8x + 36) can be expanded to 8x + 44 - 32x + 144, which corresponds to option b).
Step-by-step explanation:
To use the distributive property to write the expression 4(2x + 11 - 8x + 36) without parentheses, we apply the property by multiplying each term inside the parentheses by 4.
The distributive property states that for any numbers a, b, and c, the equality a(b + c) = ab + ac holds true. Using this property, we can expand our expression:
• 4(2x) gives us 8x,
• 4(11) gives us 44,
• 4(-8x) gives us -32x (note the change in sign), and
• 4(36) gives us 144.
Combining all these results, we get the expanded expression: 8x + 44 - 32x + 144.
Therefore, the expression without parentheses, using the distributive property, is option b) 8x + 44 - 32x + 144.