Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
-10x + 20x + 4x – 8
-8 + 24x – 10x²
4x + 20x – 10x² – 8
-10x² + 24x – 8
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Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
-10x + 20x + 4x – 8
-8 + 24x – 10x²
4x + 20x – 10x² – 8
-10x² + 24x – 8
To determine which polynomial is NOT equivalent to the expression (5x – 2)(-2x + 4), we first need to expand that expression:
1. Expand (5x – 2)(-2x + 4):
– Using the distributive property (also known as FOIL for binomials):
– ( 5x cdot -2x = -10x^2 )
– ( 5x cdot 4 = 20x )
– ( -2 cdot -2x = 4x )
– ( -2 cdot 4 = -8 )
Now, combine the terms:
[
-10x^2 + 20x + 4x – 8 = -10x^2 + 24x – 8
]
Next, we compare this polynomial (-10x^2 + 24x – 8) with each option:
1. Option 1: (-10x + 20x + 4x – 8)
– Combine: (20x – 10x + 4x – 8 = 14x – 8) (not equivalent)
2. Option 2: (-8 + 24x – 10x^2)
– This is just the rearrangement of (-10x^2 +