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CanadaON
Grade 10

Expand binomial expressions

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

Fill in the blanks to make the expression true.

Easy
< 1min

What expression makes the equation true?

Easy
< 1min
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10D.QR3.01

Expand and simplify second-degree polynomial expressions, using a variety of tools and strategies

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