The area of the figure below is $\left(y+3\right)\left(y+7\right)$(y+3)(y+7). We want to find another expression for this area by finding the sum of the areas of the four smaller rectangles.

A big rectangle segmented into four smaller rectangles. Rectangle $A$`A`, $B$`B`, $C$`C`, and $D$`D`. Rectangle $A$`A` is located at the bottom left of the big rectangle, with length and width labeled to measure $y$`y`, indicating their unknown measure. Rectangle $B$`B` is situated above $A$`A`, at the top left side of the big rectangle, with width measuring $3$3 units. The bottom side of Rectangle $B$`B` is same as the top side of Rectangle $A$`A`. Rectangle $C$`C` is located at the bottom right of the big rectangle with length measuring $7$7 units. The left side of Rectangle $C$`C` is same as the right side of Rectangle $A$`A`. Rectangle $D$`D` is situated above $C$`C`, at the right of $B$`B`, at the top right side of the big rectangle. The bottom side of Rectangle $D$`D` is same as the top side of Rectangle $C$`C`. And the left side of Rectangle $D$`D` is same as the right side of Rectangle $B$`B`.

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

2min

Fill in the blanks to make the expression true.

Easy

< 1min

Expand and simplify the following:

$-\left(x+5\right)\left(x+2\right)$−(x+5)(x+2)

Easy

1min

Expand the following perfect square: $9\left(3x+8y\right)^2$9(3x+8y)2

Easy

2min

Outcomes

1.2.4.2

expand quadratic and cubic polynomials from factors

1.08 Expansion

Interactive practice questions

Outcomes

1.2.4.2

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