Question

the area of the figure to the right is $(x+5)(x+6)$. find another expression for this area by finding the sum of the areas of the smaller rectangles.

the area is $\boldsymbol{\square}$. (simplify your answer.)

Explanation:

Step1: Calculate area of each small rectangle

Top-left: $x \times x = x^2$
Top-right: $x \times 6 = 6x$
Bottom-left: $5 \times x = 5x$
Bottom-right: $5 \times 6 = 30$

Step2: Sum all small rectangle areas

$x^2 + 6x + 5x + 30$

Step3: Combine like terms

$x^2 + (6x + 5x) + 30 = x^2 + 11x + 30$

Answer:

$x^2 + 11x + 30$