Question

the area of the figure to the right is (x + 5)(x + 8). find another expression for this area by finding the sum of the areas of the smaller rectangles. the area is □. (simplify your answer.)

Explanation:

Step1: Identify the four rectangles

The figure can be divided into four rectangles:

• Top - left: length \( x \), width \( x \), area \( x\times x = x^{2} \)
• Top - right: length \( 5 \), width \( x \), area \( 5\times x=5x \)
• Bottom - left: length \( x \), width \( 8 \), area \( x\times8 = 8x \)
• Bottom - right: length \( 5 \), width \( 8 \), area \( 5\times8=40 \)

Step2: Sum the areas of the four rectangles

Sum the areas: \( x^{2}+5x + 8x+40 \)

Step3: Combine like terms

Combine the \( x \) terms: \( x^{2}+(5x + 8x)+40=x^{2}+13x + 40 \)

We can also verify this by expanding \( (x + 5)(x + 8) \) using the distributive property (FOIL method):
\( (x+5)(x + 8)=x\times x+x\times8+5\times x + 5\times8=x^{2}+8x+5x + 40=x^{2}+13x + 40 \)

Answer:

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