Question

9c⁵(4c⁶+10c+7) Simplify your answer as much as possible. Check

Answer 1

The expression 9c⁵(4c⁶+10c+7) is simplified by distributing the 9c⁵ across the terms in the parentheses to get 36c¹¹ + 90c⁶ + 63c⁵. To check the answer, we verify the correct application of exponent rules and multiplication of coefficients.

Step-by-step explanation:

To simplify the expression 9c⁵(4c⁶+10c+7), we distribute the 9c⁵ across the terms inside the parentheses.

1. Multiply 9c⁵ by 4c⁶:
2. (9 × 4) × (c⁵ × c⁶) = 36c¹¹ (because adding the exponents when multiplying like bases).
3. Multiply 9c⁵ by 10c:
4. (9 × 10) × (c⁵ × c) = 90c⁶ (because adding the exponents when multiplying like bases).
5. Multiply 9c⁵ by 7:
6. (9 × 7) × c⁵ = 63c⁵ (since there's no c term in the 7, the c⁵ remains unchanged).

Putting it all together, the simplified expression is 36c¹¹ + 90c⁶ + 63c⁵.

To check the answer, ensure that the exponents were added correctly when multiplying the terms with like bases, and that the coefficients were multiplied correctly. In this case, all multiplications and additions are correct, so the answer is reasonable.