Exploring Algebraic Identities — Important Questions
CBSE · Class 9 · Mathematics
168 important questions from Exploring Algebraic Identities for CBSE Class 9 Mathematics, with answers. Part of the CBSE Class 9 Mathematics syllabus.
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Important Questions from Exploring Algebraic Identities
Find the side of the cube whose volume is p³ + 6p²q + 12pq² + 8q³ cubic units.
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p + 2q units
Compare p³ + 6p²q + 12pq² + 8q³ with a³ + 3a²b + 3ab² + b³. Here a = p and b = 2q. So the expression becomes (p + 2q)³. Therefore the side is p + 2q units.
Rewrite 8n³ - 60n²m + 150nm² - 125m³ as a cube of a binomial.
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(2n - 5m)³
Compare 8n³ - 60n²m + 150nm² - 125m³ with a³ - 3a²b + 3ab² - b³. Take a = 2n and b = 5m. Then the expression becomes (2n - 5m)³.
Find the sum of cubes of three numbers whose sum is 10, product is 25, and sum of squares is 38.
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145
Use x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - xz - yz). First find xy + xz + yz using (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz. So 100 = 38 + 2(xy + xz + yz), giving xy + xz + yz = 31. Then x³ + y³ + z³ - 75 = 10(38 - 31) = 70, so x³ + y³ + z³ = 145.
Find the factors of x² + 11x + 30.
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(x + 5)(x + 6)
Find two numbers whose sum is 11 and product is 30. The pair 5 and 6 works because 5 + 6 = 11 and 5 × 6 = 30. So x² + 11x + 30 = (x + 5)(x + 6).
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- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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