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Question 1.Factorize Solution:i. y³ – 27= y³ – (3)³Here, a = y and b = 3∴ y³ – 27 = (y – 3)[y² + y(3) + (3)2]…[∵ a³ – b³ = (a – b) (a² + ab + b²)]= (y – 3)(y² + 3y + 9) ii. x³ – 64y³= x³ – (4y)³Here, a = … Read more

Question 1.Factorise:i. x³ + 64y³ii. 125p³ + q³iii. 125k³ + 27m³iv. 2l³ + 432m³v. 24a³ + 81b³ Solution:i. x³ + 64y³= x³ + (4y)³Here, a = x and b = 4y∴ x³ + 64y³ = (x + 4y) [x² – x(4y) + (4y)²]….[∵ a³ + b³ = (a + b)(a² – ab + b²)]= (x … Read more

Question 1.Factorize:i. x² + 9x + 18ii. x² – 10x + 9iii. y² + 24y + 144iv. 5y² + 5y – 10v. p² – 2p – 35vi. p² – 7p – 44vii. m² – 23m + 120viii. m² – 25m + 100ix. 3x² + 14x + 15x. 2x² + x – 45xi. 20x² – 26x … Read more

Question 1.Expand:i. (2p + q + 5)²ii. (m + 2n + 3r)²iii. (3x + 4y – 5p)²iv. (7m – 3n – 4k)²Solution:i. (2p + q + 5)² = (2p)² + (q)² + (5)² + 2(2p) (q) + 2(q) (5) + 2(2p) (5)… [(a + b + c)² = a² + b² + c² + 2ab … Read more

Question 1.Expand:i. (2m – 5)³ii. (4 – p)³iii. (7x – 9y)³iv. (58)³v. (198)³ Solution:i. Here, a = 2m and b = 5(2m – 5)³= (2m)³ – 3(2m)² (5) + 3(2m) (5)² – (5)³… [(a – b)³ = a³ – 3a²b + 3ab² – b³]= 8m³ – 3(4m²)(5) + 3(2m)(25) – 125= 8m³ – 60m² + … Read more

Question 1.Expand:i. (k + 4)³ii. (7x + 8y)³iii. (7x + m)³iv. (52)³v. (101)³ Solution:i. Here, a = k and b = 4(k + 4)³ = (k)³ + 3(k)² (4) + 3(k)(4)² + (4)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= k³ + 12k² + 3(k)(16) + 64= k³ + 12k² + … Read more

Question 1.Expand :i. (a + 2)(a – 1)ii. (m – 4)(m + 6)iii. (p + 8) (p – 3)iv. (13 + x)(13 – x)v. (3x + 4y) (3x + 5y)vi. (9x – 5t) (9x + 3t) Solution:i. (a + 2)(a – 1)= a² + (2 – 1) a + 2 × (-1)..[∵ (x + A) … Read more

Chapter 4 Altitudes and Medians of a Triangle Question 1.In ∆LMN, ___ is an altitude and __ is a median, (write the names of appropriate segments.) Solution:In ∆LMN, seg LX is an altitude and seg LY is a median. Question 2.Draw an acute angled ∆PQR. Draw all of its altitudes. Name the point of concurrence … Read more

Question 1.Find the cube root of the following numbers.i. 8000ii. 729iii. 343iv. -512v. -2744vi. 32768Solution:i. 8000= 2 × 2 × 2 × 10 × 10 × 10= (2 × 10) × (2 × 10) × (2 × 10)= (2 × 10)³= 20³ ii. 729= (3 × 3) × (3 × 3) × (3 × 3)= … Read more

Chapter 3 Indices and Cube Root Set 3.2 Question 1.Complete the following table. Solution:  Question 2.Write the following numbers in the form of rational indices.i. Square root of 5th power of 121.ii. Cube of 4th root of 324.iii. 5th root of square of 264.iv. Cube of cube root of 3.Solution: