Question

1. (x + 5)(x + 8)

1. tyler drew a diagram to expand (x + 5)(2x + 3).

a. explain tylers mistake.
b. what is the correct expanded form (product) of ?

Explanation:

Problem 1: Expand \((x + 5)(x + 8)\)

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(x \times x = x^2\)
Multiply the Outer terms: \(x \times 8 = 8x\)
Multiply the Inner terms: \(5 \times x = 5x\)
Multiply the Last terms: \(5 \times 8 = 40\)

Step2: Combine like terms

Add the outer and inner terms: \(8x + 5x = 13x\)
Combine all terms: \(x^2 + 13x + 40\)

When expanding \((x + 5)(2x + 3)\), the distributive property (FOIL or area model) requires multiplying each term in the first binomial by each term in the second. A common mistake is miscalculating the product of \(5\) and \(2x\) (or another term), or miscombining like terms. For example, if Tyler forgot to multiply \(5\) by \(2x\) (in an area model, missing a region) or added coefficients incorrectly, that would be the error. Typically, in expanding \((x + 5)(2x + 3)\), the correct distribution is \(x(2x) + x(3) + 5(2x) + 5(3)\); if Tyler omitted \(5(2x)\) or miscalculated it, that’s the mistake.

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(x \times 2x = 2x^2\)
Multiply the Outer terms: \(x \times 3 = 3x\)
Multiply the Inner terms: \(5 \times 2x = 10x\)
Multiply the Last terms: \(5 \times 3 = 15\)

Step2: Combine like terms

Add the outer and inner terms: \(3x + 10x = 13x\)
Combine all terms: \(2x^2 + 13x + 15\)

Answer:

\(x^2 + 13x + 40\)

Problem 2a: Explain Tyler’s mistake (assuming Tyler’s diagram had an error in distribution)