Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
-10x + 20x + 4x – 8
4x + 20x – 10x² – 8
-8 + 24x – 10x²
-10x² + 24x – 8
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To determine which polynomial is NOT equivalent to (5x – 2)(-2x + 4), we first need to expand the expression.
1. Expand (5x – 2)(-2x + 4):
– Multiply the first terms: ( 5x times -2x = -10x^2 )
– Multiply the outer terms: ( 5x times 4 = 20x )
– Multiply the inner terms: ( -2 times -2x = 4x )
– Multiply the last terms: ( -2 times 4 = -8 )
Now, combine all the terms:
[
-10x^2 + 20x + 4x – 8 = -10x^2 + 24x – 8
]
So, (5x – 2)(-2x + 4) simplifies to:
[
-10x^2 + 24x – 8
]
Next, let’s analyze the given options:
1. Option 1: (-10x + 20x + 4x – 8) simplifies to (14x – 8).
2. Option 2: (4x + 20x – 10x^2 – 8) is equivalent to (-10x^2 + 24x – 8).
3.