Question

problem 2: complete the area model
keep working on it.
$x^{2}-25=$
rectangle
expression
1
$x^{2}$
11
$5x$
111
iv
-25
check expressions

Explanation:

Step1: Factor the expression \(x^{2}-25\)

We know that \(a^{2}-b^{2}=(a + b)(a - b)\). Here \(a=x\) and \(b = 5\), so \(x^{2}-25=(x + 5)(x - 5)\).

Step2: Expand \((x + 5)(x - 5)\) using the area - model (FOIL method)

• First: \(x\times x=x^{2}\) (Rectangle I)
• Outer: \(x\times(- 5)=-5x\) (Rectangle III)
• Inner: \(5\times x = 5x\) (Rectangle II)
• Last: \(5\times(-5)=-25\) (Rectangle IV)

Answer:

\((x + 5)(x - 5)\)