Question

An expression is shown/

4(34x+3x−2)−2(3x2+1+3x)

Rewrite an equivalent expression with the fewest terms possible

(3 points)
x2
+
x−

Answer 1

To simplify the expression \( 4(34x + 3x - 2) - 2(3x^2 + 1 + 3x) \), we'll distribute and then combine like terms.

1. Distribute \( 4 \) in the first part:
\[
4(34x + 3x - 2) = 4(34x) + 4(3x) - 4(2) = 136x + 12x - 8 = 148x - 8
\]

2. Distribute \( -2 \) in the second part:
\[
-2(3x^2 + 1 + 3x) = -2(3x^2) - 2(1) - 2(3x) = -6x^2 - 2 - 6x
\]

3. Now combine the two results:
\[
(148x - 8) + (-6x^2 - 2 - 6x) = -6x^2 + 148x - 6x - 8 - 2
\]

4. Combine like terms:
\[
-6x^2 + (148x - 6x) + (-8 - 2) = -6x^2 + 142x - 10
\]

Thus, the expression simplifies to:
\[
-6x^2 + 142x - 10
\]

This is the equivalent expression with the fewest terms possible.

If you prefer to present it in standard form, you can write it as:
\[
-6x^2 + 142x - 10
\]

Where we may leave it in that format or ask for additional reductions based on specific goals.