If C, equals, minus, 3, plus, 5, s, squaredC=−3+5s

Question

2
and B, equals, minus, 2, s, plus, 5, commaB=−2s+5, find an expression that equals 2, C, plus, 3, B2C+3B 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 solve the problem using the structure given in your example, we will start from the definitions of \( C \) and \( B \):

1. Given: \[ C = -3 + 5s^2 \] \[ B = -2s + 5 \]

2. We need to find \( 2C + 3B \):

   \[ 2C + 3B = 2(-3 + 5s^2) + 3(-2s + 5) \]

3. Calculate \( 2C \): \[ 2C = 2(-3 + 5s^2) = -6 + 10s^2 \]

4. Calculate \( 3B \): \[ 3B = 3(-2s + 5) = -6s + 15 \]

5. Now, combine \( 2C \) and \( 3B \): \[ 2C + 3B = (-6 + 10s^2) + (-6s + 15) \]

6. Combine the terms:

   • Combine the constant terms: \(-6 + 15 = 9\)
   • Combine the \( s \) terms: \(-6s\)
   • The \( s^2 \) term remains as \( 10s^2 \)

   Thus, the expression becomes: \[ 2C + 3B = 10s^2 - 6s + 9 \]

Finally, the expression \( 2C + 3B \) in standard form is: \[ 10s^2 - 6s + 9 \]