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Expansions — Flashcards

ICSE · Class 9 · Mathematics

25 flashcards for Expansions (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Solve using expansion: (a+b)(a+b)"

43 questions25 flashcards12 formulas & key relations5 concepts

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A geometric representation showing how (a+b)² expands to a² + 2ab + b² using areas of squares and rectangles.
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25 Flashcards·
Square of sumSquare of differenceIdentity verification
Card 1Square of sum

Solve using expansion: (a+b)(a+b)

Answer

Step 1: Multiply each term in the first bracket by each term in the second bracket. Step 2: (a+b)(a+b) = a(a+b) + b(a+b) Step 3: = a^2 + ab + ab + b^2 Step 4: Combine like terms: a^2 + 2ab + b^2 Answe…

Card 2Square of difference

Solve: Expand (a-b)^2

Answer

Step 1: Write it as (a-b)(a-b). Step 2: Multiply term by term. Step 3: (a-b)(a-b) = a^2 - ab - ab + b^2 Step 4: Combine like terms: a^2 - 2ab + b^2 Answer: (a-b)^2 = a^2 - 2ab + b^2…

Card 3Square of sum

Apply the square of sum identity to find (5+3)^2.

Answer

Step 1: Use (a+b)^2 = a^2 + 2ab + b^2. Step 2: Let a = 5 and b = 3. Step 3: 5^2 + 2×5×3 + 3^2 = 25 + 30 + 9 Step 4: Add the terms: 64 Answer: (5+3)^2 = 64…

Card 4Square of sum

Apply the square of sum identity to find (-8+5)^2.

Answer

Step 1: Use (a+b)^2 = a^2 + 2ab + b^2. Step 2: Let a = -8 and b = 5. Step 3: (-8)^2 + 2×(-8)×5 + 5^2 = 64 - 80 + 25 Step 4: Add carefully: 9 Answer: (-8+5)^2 = 9…

Card 5Identity verification

Solve by expansion: (a+b)^2 when a = 5 and b = 3, and check the result in both forms.

Answer

Step 1: Direct form: (5+3)^2 = 8^2 = 64. Step 2: Expanded form: 5^2 + 2×5×3 + 3^2 = 25 + 30 + 9 = 64. Step 3: Both forms give the same result. Answer: 64, so the identity is verified for these values.

Card 6Identity verification

Solve by expansion: (a+b)^2 when a = -8 and b = 5, and check the result in both forms.

Answer

Step 1: Direct form: (-8+5)^2 = (-3)^2 = 9. Step 2: Expanded form: (-8)^2 + 2×(-8)×5 + 5^2 = 64 - 80 + 25 = 9. Step 3: Both forms give the same result. Answer: 9, so the identity is verified for these…

Card 7Square of sum

What is the expansion of (a+b)^2?

Answer

Formula: (a+b)^2 = a^2 + 2ab + b^2 Meaning of terms: a and b are any real numbers. Quick example: if a = 2 and b = 1, then (2+1)^2 = 9 and a^2 + 2ab + b^2 = 4 + 4 + 1 = 9.

Card 8Square of difference

What is the expansion of (a-b)^2?

Answer

Formula: (a-b)^2 = a^2 - 2ab + b^2 Meaning of terms: a and b are any real numbers. Quick example: if a = 6 and b = 2, then (6-2)^2 = 16 and a^2 - 2ab + b^2 = 36 - 24 + 4 = 16.

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Frequently Asked Questions

What are the important topics in Expansions for ICSE Class 9 Mathematics?
Key topics in Expansions include Core ideas and identities, Worked verification of the main identity, Reciprocal identities and their use. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Expansions?
There are 25 flashcards for Expansions covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Expansions for Class 9 exams?
Learn the core ideas first, then work through the 43 practice questions on Expansions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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