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Binomial Expansion Introduction
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Binomial Expansion Introduction
Expand each squared binomial. Show your working where space is provided. For multiple-select questions, choose every correct option.
Understanding the Area Model
1.A square has side lengths (r + s). Which expression gives its total area?
- r² + s²
- r² + 2rs + s²
- 2r + 2s
- r² + rs + s²
2.A square with side length (x + 5) is divided into four rectangles. Which dimensions describe all four rectangles? Select every correct option.
- x by x
- x by 5
- 5 by 5
- x by 10
- 5 by x
3.In the expansion of (k + 6)², what is the combined area of the two identical rectangular sections?
- 6k
- 12k
- k² + 36
- 2k + 12
4.Match each squared binomial to its expanded form.
- (z + 2)²
- (z + 5)²
- (z + 3)²
- (z + 1)²
- z² + 10z + 25
- z² + 2z + 1
- z² + 6z + 9
- z² + 4z + 4
Draw and Expand
5.Complete the expansion: (q + 7)² = q² + + 49.
Draw a square area model for (w + 3)². Label its side lengths and write the area inside each of the four sections.
6.Expand (w + 3)².
7.Expand (d + 8)².
8.Expand (4 + h)².
9.Expand (c + 2)².
10.In your own words, describe how the four parts of an area model for a squared binomial combine to make its expansion.
Apply the Pattern
11.A square has side length (n + 9), and one of its four regions has area n². Find the combined area of the two rectangular regions.
12.Explain why (u + v)² is not equal to u² + v². Use u = 2 and v = 3 to check the two expressions.
3 printable pages
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