If C, equals, x, plus, 6C=x+6 and D, equals, 3, x, minus, 6, plus, 4, x, squared, commaD=3x−6+4x

Question

2
, find an expression that equals C, plus, 3, DC+3D in standard form.

Solve the problem just like the example below
⬇️
If C, equals, 3, x, squared, plus, 4, x
C=3x
2
+4x and
B, equals, 2, x, squared, minus, 7, comma
B=2x
2
−7, find an expression that equals
2, C, plus, 2, B
2C+2B in standard form.
C, equals, 3, x, squared, plus, 4, x
C=
3x
2
+4x
B, equals, 2, x, squared, minus, 7
B=
2x
2
−7
2, C, plus, 2, B
2C+2B
2, left parenthesis, 3, x, squared, plus, 4, x, right parenthesis, plus, 2, left parenthesis, 2, x, squared, minus, 7, right parenthesis
2(3x
2
+4x)+2(2x
2
−7)
6, x, squared, plus, 8, x, plus, 4, x, squared, minus, 14
6x
2
+8x+4x
2
−14
10, x, squared, plus, 8, x, minus, 14
10x
2
+8x−14

Answer 1

To find \( C + 3D \), we first need to determine the expressions for \( C \) and \( D \) as given in the problem.

1. Finding \( C \): \[ C = x + 6 \]

2. Finding \( D \): \[ D = 3x - 6 + 4x^2 \] This can also be rearranged to: \[ D = 4x^2 + 3x - 6 \]

3. Calculating \( C + 3D \): \[ C + 3D = (x + 6) + 3(4x^2 + 3x - 6) \]

   Now, distribute \( 3 \) in \( 3D \): \[ 3(4x^2 + 3x - 6) = 12x^2 + 9x - 18 \]

   Combining this with \( C \): \[ C + 3D = (x + 6) + (12x^2 + 9x - 18) \]

   Now combine like terms: \[ C + 3D = 12x^2 + (1x + 9x) + (6 - 18) \] \[ = 12x^2 + 10x - 12 \]

4. Final Result: The expression for \( C + 3D \) in standard form is: \[ \boxed{12x^2 + 10x - 12} \]