Question

match the multiplication problem on the left with its product on the right.
not all options will be used.
(3 points)
$(x - 5)(x + 4)$
$(x - 2)(x + 5)$
$-5(x + 4)$
$5x + 20$ $x^2 + 3x - 10$ $x^2 - x - 20$ $x^2 + 10x + 3$ $5x + 4$ $x^2 - 9x - 20$

Explanation:

Step1: Expand \((x - 5)(x + 4)\)

Using the distributive property (FOIL method): \(x\times x + x\times4 - 5\times x - 5\times4\)
\(= x^2 + 4x - 5x - 20\)
\(= x^2 - x - 20\)

Step2: Expand \((x - 2)(x + 5)\)

Using the distributive property (FOIL method): \(x\times x + x\times5 - 2\times x - 2\times5\)
\(= x^2 + 5x - 2x - 10\)
\(= x^2 + 3x - 10\)

Step3: Expand \(-5(x + 4)\)

Using the distributive property: \(-5\times x + (-5)\times4\)
\(= -5x - 20\)? Wait, no, the original is \(-5(x + 4)\)? Wait, the problem has \(-5(x + 4)\)? Wait, maybe it's a typo, but if it's \(5(x + 4)\) (maybe a sign error), but following the given: Wait, the left side is \(-5(x + 4)\)? Wait, no, the user's image shows \(-5(x + 4)\)? Wait, no, looking back: the third left is \(-5(x + 4)\)? Wait, but the options have \(5x + 20\). Wait, maybe it's \(5(x + 4)\). Let's assume it's \(5(x + 4)\) (maybe a sign mistake in the problem). Then:
Using distributive property: \(5\times x + 5\times4 = 5x + 20\)

Answer:

• \((x - 5)(x + 4)\) matches \(x^2 - x - 20\)
• \((x - 2)(x + 5)\) matches \(x^2 + 3x - 10\)
• \(-5(x + 4)\) (assuming it's \(5(x + 4)\) for the option \(5x + 20\)) matches \(5x + 20\) (if the left side is \(5(x + 4)\); if it's \(-5(x + 4)\), the result is \(-5x - 20\), which is not an option, so likely a typo and it's \(5(x + 4)\))