The area of the figure below is $\left(y+3\right)\left(y+6\right)$(y+3)(y+6). We want to find another expression for this area by finding the sum of the areas of the four smaller rectangles.

A rectangle is divided by a vertical and horizontal line into four smaller rectangles, rectangles $A$`A`, $B$`B`, $C$`C`, and $D$`D`. The horizontal line divides the width of the rectangle into two width as labeled on the left side. The upper width is labeled $3$3 units. The lower width is labeled $y$`y` units. The vertical line divides the length of the rectangle into two lengths as labeled on the bottom side. The horizontal length to the left of the vertical line is labeled $y$`y` units. The horizontal length to the right of the vertical line is labeled $6$6 units. The top-left rectangle is labeled $B$`B` and has a light blue fill. The top-right rectangle is labeled $D$`D` and has a light purple fill. The bottom-left rectangle is labeled $A$`A` and has a light green fill. The bottom-right rectangle is labeled $C$`C` and has a light blue fill.

What is the area of rectangle $A$A?

What is the area of rectangle $B$B?

What is the area of rectangle $C$C?

What is the area of rectangle $D$D?

Using the areas of each rectangle, write an equivalent expression for the area of the figure.

Easy

2 min

Fill in the blanks to make the expression true.

Easy

1 min

Which of the following expressions is equivalent to $\left(y-5\right)\left(y-8\right)$(y−5)(y−8)?

Easy

< 1 min

Expand and simplify the following:

$\left(x+2\right)\left(x+6\right)$(x+2)(x+6)

Easy

1 min

Outcomes

9.C1.4

Simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts.

3.07 Binomial expansions

Interactive practice questions

Outcomes

9.C1.4

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