Question

If C=x^{2}-4C=x

2
−4 and D=2-x,D=2−x, find an expression that equals 2C+2D2C+2D in standard form.

Answer 1

To find an expression that equals 2C + 2D in standard form, we need to substitute the given expressions for C and D into the expression 2C + 2D. Here's the step-by-step solution:

1. Given C = x^2 - 4 and D = 2 - x, we can substitute these values into the expression 2C + 2D.

2. Substitute C with x^2 - 4 and D with 2 - x to get: 2(x^2 - 4) + 2(2 - x).

3. Distribute the 2 to both terms inside the parentheses: 2x^2 - 8 + 4 - 2x.

4. Combine like terms: 2x^2 - 2x + 4 - 8.

5. Simplify further: 2x^2 - 2x - 4.

6. Rearrange the terms in standard form: 2x^2 - 2x - 4.

Therefore, the expression that equals 2C + 2D in standard form is 2x^2 - 2x - 4.

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