Question

find the product.
$(x^2 + 4x)(-2x + 1)$
$?x^3 + \square x^2 + \square x$

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first polynomial by each term in the second polynomial:
\(x^2(-2x) + x^2(1) + 4x(-2x) + 4x(1)\)

Step2: Simplify each term

• \(x^2(-2x) = -2x^3\)
• \(x^2(1) = x^2\)
• \(4x(-2x) = -8x^2\)
• \(4x(1) = 4x\)

Step3: Combine like terms

Combine the \(x^2\) terms: \(x^2 - 8x^2 = -7x^2\)

So the expanded form is \(-2x^3 - 7x^2 + 4x\)

Answer:

For the \(x^3\) term: \(-2\)
For the \(x^2\) term: \(-7\)
For the \(x\) term: \(4\)

(If only the coefficient of \(x^3\) is needed as per the green box, the answer is \(-2\))