topic badge
iGCSE (2021 Edition)

5.02 Expansion

Interactive practice questions

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 rectangle segmented into four quadrilaterals: square $A$A, and rectangles $B$B, $C$C, and $D$D. Square $A$A is located at the bottom left with sides of length $y$y, while rectangle $B$B, situated above $A$A, has a length of $y$y and a width of $3$3. To the right of $A$A, rectangle $C$C has a length of $7$7 and a width of $y$y, and rectangle $D$D, positioned above $C$C, has dimensions of $7$7 by $3$3. This layout represents the algebraic expression $\left(y+7\right)\left(y+3\right)$(y+7)(y+3), with the rectangle's length being $y+7$y+7 and its width $y+3$y+3.
a

What is the area of rectangle $A$A?

b

What is the area of rectangle $B$B?

c

What is the area of rectangle $C$C?

d

What is the area of rectangle $D$D?

e

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
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

What is Mathspace

About Mathspace