Question

simplify the following expression.
$(x^2 + 4x - 5)(2x + 8)$
$?x^3 + \square x^2 + \square x + \square$

Explanation:

Step1: Distribute \(x^2\) in the first polynomial

Multiply \(x^2\) with each term in \((2x + 8)\): \(x^2\times2x = 2x^3\), \(x^2\times8 = 8x^2\)

Step2: Distribute \(4x\) in the first polynomial

Multiply \(4x\) with each term in \((2x + 8)\): \(4x\times2x = 8x^2\), \(4x\times8 = 32x\)

Step3: Distribute \(-5\) in the first polynomial

Multiply \(-5\) with each term in \((2x + 8)\): \(-5\times2x = -10x\), \(-5\times8 = -40\)

Step4: Combine like terms

• For \(x^3\) term: Only \(2x^3\), so coefficient is \(2\).
• For \(x^2\) terms: \(8x^2 + 8x^2 = 16x^2\), so coefficient is \(16\).
• For \(x\) terms: \(32x - 10x = 22x\), so coefficient is \(22\).
• For constant term: \(-40\), so constant is \(-40\).

Answer:

The coefficient of \(x^3\) is \(2\), \(x^2\) is \(16\), \(x\) is \(22\), and the constant term is \(-40\). So the filled expression is \(2x^3 + 16x^2 + 22x - 40\) (for the first box, the answer is \(2\)).