Questions: (x-4)(x^2+7x-1)=

Solution Steps

To expand the expression \((x-4)(x^2+7x-1)\), we will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial. This involves distributing \(x\) and \(-4\) across the terms in the trinomial \(x^2 + 7x - 1\).

To expand the expression \((x-4)(x^2+7x-1)\), we distribute each term in the binomial \((x-4)\) across each term in the trinomial \((x^2+7x-1)\).

1. Multiply \(x\) by each term in the trinomial:

   • \(x \cdot x^2 = x^3\)
   • \(x \cdot 7x = 7x^2\)
   • \(x \cdot (-1) = -x\)

2. Multiply \(-4\) by each term in the trinomial:

   • \(-4 \cdot x^2 = -4x^2\)
   • \(-4 \cdot 7x = -28x\)
   • \(-4 \cdot (-1) = 4\)

3. Combine the results:

   • \(x^3 + 7x^2 - x - 4x^2 - 28x + 4\)

Combine like terms:

• \(x^3\) remains as is.
• Combine \(7x^2\) and \(-4x^2\) to get \(3x^2\).
• Combine \(-x\) and \(-28x\) to get \(-29x\).
• The constant term is \(4\).

Thus, the expanded expression is: \[ x^3 + 3x^2 - 29x + 4 \]

Final Answer