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Expansions

ICSE · Class 9 · Mathematics

Flashcards for Expansions — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions20 flashcards5 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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20 Flashcards
Card 1Introduction to Expansions

What is expansion in algebra?

Answer

Expansion is the process in which the contents of brackets are evaluated. It involves multiplying out the terms inside brackets to get a simplified expression without brackets.

Card 2Basic Identities

What is the expansion of (a + b)²?

Answer

(a + b)² = a² + 2ab + b². This is derived by multiplying (a + b) with itself: (a + b)(a + b) = a² + ab + ab + b² = a² + 2ab + b²…

Card 3Basic Identities

What is the expansion of (a - b)²?

Answer

(a - b)² = a² - 2ab + b². This follows the same pattern as (a + b)² but with negative terms due to the subtraction.

Card 4Identities

What is an algebraic identity?

Answer

An equation which is true for all values of its variables is called an identity. For example, (a + b)² = a² + 2ab + b² is true for any values of a and b.

Card 5Applications

Expand (x + 5)²

Answer

(x + 5)² = x² + 2(x)(5) + 5² = x² + 10x + 25. Using the identity (a + b)² = a² + 2ab + b² where a = x and b = 5.

Card 6Applications

Expand (2x - 3)²

Answer

(2x - 3)² = (2x)² - 2(2x)(3) + 3² = 4x² - 12x + 9. Using the identity (a - b)² = a² - 2ab + b² where a = 2x and b = 3.

Card 7Derived Identities

What is the result of (a + b)² + (a - b)²?

Answer

(a + b)² + (a - b)² = 2(a² + b²). This is derived by adding the expansions: (a² + 2ab + b²) + (a² - 2ab + b²) = 2a² + 2b² = 2(a² + b²)…

Card 8Derived Identities

What is the result of (a + b)² - (a - b)²?

Answer

(a + b)² - (a - b)² = 4ab. This is derived by subtracting: (a² + 2ab + b²) - (a² - 2ab + b²) = 4ab…

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What are the important topics in Expansions for ICSE Class 9 Mathematics?
Expansions covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
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