Simplify the expression. Write your answer is standard form. −4d(5d2−12)+7(d+5)-4𝑑(5𝑑2-12)+7(𝑑+5)

1. Break Down the Problem

We need to simplify the expression: $-4d(5d^2 - 12) + 7(d + 5) - 4d(5d^2 - 12) + 7(d + 5)$

2. Relevant Concepts

In order to simplify, we'll distribute, combine like terms, and simplify further using standard algebraic principles.

3. Analysis and Detail

1. Distributing $-4d$: $-4d(5d^2 - 12) = -20d^3 + 48d$

2. Distributing $7$: $7(d + 5) = 7d + 35$

3. Combine like terms from both distributions: The original expression can be rewritten with the calculated distributions: $-20d^3 + 48d + 7d + 35 - 20d^3 + 48d + 7d + 35$

4. Combining like terms:

   • Combining $d^3$ terms: $-20d^3 - 20d^3 = -40d^3$
   • Combining $d$ terms: $48d + 7d + 48d + 7d = 110d$
   • Combining constant terms: $35 + 35 = 70$

4. Verify and Summarize

The combined expression is: $-40d^3 + 110d + 70$

Final Answer

Thus, the simplified expression in standard form is: $\boxed{-40d^3 + 110d + 70}$