Question

Hey is a destructive property to prove that these algebraic pressure expressions are equivalent explain your answer in one sentence for each expression and show your work expression one x - 5 x + 3 expression 2 two x power 2 minus x power 2 - 2x -20 + 9

Answer 1

To prove that the two algebraic expressions are equivalent, we can simplify each expression and compare the results.

**Expression 1**: \( x - 5x + 3 \)

1. Combine like terms:
\[
x - 5x = -4x
\]
So,
\[
-4x + 3
\]

**Expression 2**: \( 2x^2 - x^2 - 2x - 20 + 9 \)

1. Start by combining the \( x^2 \) terms:
\[
2x^2 - x^2 = x^2
\]
2. Now, simplify the expression:
\[
x^2 - 2x - 20 + 9 = x^2 - 2x - 11
\]

**Comparison**:
- Expression 1: \( -4x + 3 \)
- Expression 2: \( x^2 - 2x - 11 \)

Since neither expressions simplify to a common form, they are not equivalent.

**In conclusion**: Expression 1 yields a linear expression while Expression 2 yields a quadratic expression, indicating they are algebraically distinct.