Expansions
ICSE · Class 9 · Mathematics
Flashcards for Expansions — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setSolve 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…
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…
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…
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…
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.
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…
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.
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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