Question

If C=q²-2+qC=q 2 -2+q and D=3q²+2q,D=3q 2 +2q, find an expression that equals 3C-3D³C-3D in standard form.

Answer 1

To find an expression for 3C - 3D, where C = q² - 2 + q and D = 3q² + 2q, we calculate 3C and -3D separately and then combine them to get the final expression in standard form: -6q² - 6.

Step-by-step explanation:

The student is asking to find an expression for 3C - 3D where C is defined as C = q² - 2 + q and D is defined as D = 3q² + 2q. To simplify this expression, let's first multiply both C and D by 3.

First, for 3C we have:

• 3C = 3(q² - 2 + q)
• 3C = 3q² - 6 + 3q

And for -3D, we have:

• -3D = -3(3q² + 2q)
• -3D = -9q² - 6q

Now, combining the expressions for 3C and -3D:

• 3C - 3D = (3q² - 6 + 3q) - (9q² + 6q)
• 3C - 3D = 3q² - 9q² - 6 + 6q - 6q
• 3C - 3D = -6q² - 6

Therefore, the expression in standard form for 3C - 3D is -6q² - 6.