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Binomial Expansion Area Models
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Binomial Expansion Area Models
Use the area models to identify and expand squared binomials. Show your working where space is provided.
Understanding Area Models
1.A square has side length a + b and is divided into four rectangles. Which list gives the area of each region?
- a², ab, ab, b²
- a², 2ab, b²
- a, b, a, b
- a², b², 2a, 2b
2.Expand (t + 4)².
- t² + 8t + 16
- t² + 4t + 16
- t² + 16
- t² + 8t + 8
3.In the four-part area model for (p + q)², how many regions have area pq?
- One
- Two
- Three
- Four
4.Select the two regions that represent squared terms in the area model of (r + s)².
- The r-by-r region
- One r-by-s region
- The s-by-s region
- The other r-by-s region
Drawing and Expanding
5.Draw a square area model for (x + 3)². Label the side lengths and write the area in each of the four regions.
6.Use the area model of (x + 3)² to write the expansion in simplified form.
7.Expand (z + 6)² by finding the four region areas and combining like terms.
8.In a sentence or two, explain why the expansion of (u + v)² includes a 2uv term.
Challenge and Further Practice
9.A corner square in an area model has area 25 cm². What is the length of one side of that corner square?
10.Use multiplication or an area model to expand (m + n + 2)². Collect like terms.
11.Expand (2x − 5)².
12.Expand (3y + 2)(3y − 2).
- 9y² − 4
- 9y² + 12y + 4
- 6y² − 4
- 9y² − 12y + 4
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