Expand binomial expressions

Lesson

Practice

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 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

Fill in the blanks to make the expression true.

Easy

< 1min

What expression makes the equation true?

Easy

< 1min

Outcomes

12CT.B.3.4

Expand and simplify polynomial expressions involving more than one variable [e.g., simplify – 2xy(3x^2 y^3 – 5x^3 y^2 )], including expressions arising from real-world applications

Expand binomial expressions

Interactive practice questions

Outcomes

12CT.B.3.4

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