use the distributive property to rewrite the polynomial (2x+1)(x-4)

Answer 1

To use the distributive property to rewrite the polynomial \((2x + 1)(x - 4)\), we will distribute each term in the first polynomial by each term in the second polynomial.

1. Distributing \(2x\) to both terms in \((x - 4)\): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-4) = -8x \]

2. Distributing \(1\) to both terms in \((x - 4)\): \[ 1 \cdot x = x \] \[ 1 \cdot (-4) = -4 \]

Now combine all the results: \[ 2x^2 - 8x + x - 4 \]

Next, combine like terms \(-8x + x\): \[ 2x^2 - 7x - 4 \]

So, the polynomial \((2x + 1)(x - 4)\) rewritten is: \[ \boxed{2x^2 - 7x - 4} \]

Answer 2

2 is right but the other ones are not

Answer 3

Let's redo the calculation for \((2x + 1)(x - 4)\) using the distributive property step by step.

1. Distribute \(2x\) over \((x - 4)\):

   • \(2x \cdot x = 2x^2\)
   • \(2x \cdot (-4) = -8x\)

2. Distribute \(1\) over \((x - 4)\):

   • \(1 \cdot x = x\)
   • \(1 \cdot (-4) = -4\)

Now, we combine all these terms: \[ 2x^2 - 8x + x - 4 \]

Next, combine the like terms \(-8x + x\): \[ 2x^2 - 7x - 4 \]

The final rewritten polynomial is: \[ \boxed{2x^2 - 7x - 4} \]

Please let me know if there's something specific you believe is incorrect or if there's further clarification needed!