Question

If B, equals, k, minus, 5, k, squared, minus, 1B=k−5k
2
−1 and C, equals, k, minus, 2, k, squared, commaC=k−2k
2
, find an expression that equals 2, B, plus, 3, C2B+3C 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

Let's solve the problem step by step.

We are given:
- \( B = k - 5k^2 - 1 \)
- \( C = k - 2k^2 \)

We need to find the expression for \( 2B + 3C \).

### Step 1: Substitute the expressions for B and C

First, we will substitute the expressions for \( B \) and \( C \) into \( 2B + 3C \).

\[
2B + 3C = 2(k - 5k^2 - 1) + 3(k - 2k^2)
\]

### Step 2: Distribute the coefficients

Now, we will distribute the 2 and 3 to the respective expressions:

\[
2B = 2(k - 5k^2 - 1) = 2k - 10k^2 - 2
\]
and
\[
3C = 3(k - 2k^2) = 3k - 6k^2
\]

### Step 3: Combine the expressions

Now we will combine \( 2B \) and \( 3C \):

\[
2B + 3C = (2k - 10k^2 - 2) + (3k - 6k^2)
\]

Combine like terms:

\[
= (2k + 3k) + (-10k^2 - 6k^2) - 2
\]

This simplifies to:

\[
= 5k - 16k^2 - 2
\]

### Step 4: Write in standard form

In standard form, we typically write polynomials starting with the highest degree term. Therefore, we rearrange it:

\[
= -16k^2 + 5k - 2
\]

### Final Result

The expression that equals \( 2B + 3C \) in standard form is:

\[
-16k^2 + 5k - 2
\]