Question

If D = 2 - 9n² and C = n + 3 + 4n², find an expression that equals 3D - C in standard form.

Answer 1

To find an expression for 3D - C in standard form, triple D, subtract C, and combine like terms to obtain the result -31n² - n + 3.

Step-by-step explanation:

To find an expression that equals 3D - C in standard form, where D = 2 - 9n² and C = n + 3 + 4n², we should first expand and multiply the given expressions.

First, triple the expression for D: 3D = 3(2 - 9n²) = 6 - 27n².

Now, subtract the expression for C from this result: 3D - C = (6 - 27n²) - (n + 3 + 4n²).

Combine like terms: 3D - C = 6 - 27n² - n - 3 - 4n² = 3 - 31n² - n.

Finally, to write it in standard form (with decreasing powers of n), we get: 3D - C = -31n² - n + 3.