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C7 7.1
- 1. Question 1. 2x2 and 12x2 Solution: 2x2 and 12x2 HCF of 2 and 12 =2 HCF of x2 ,x2 =x2 ∴ HCF = 2x2 Question 2. (6xy3 and 18x2 y3 Solution: 6x3 y and 18xy HCF of 6, 18 = 6 HCF of x3 and x2 = x2 HCF of y and y3 -y ∴ HCF = 6x2 y Question 3. 7x, 21x2 and 14xy2 Solution: 7x, 21x2 and 14xy2 HCF of 7, 21 and 14 = 7 HCF of x, x2 , x = x ∴ HCF = 7x Question 4. 42x2 yz and 63x3 y2 z3 Solution: 42x2 yz and 63x3 y2 z3 HCF of 42 and 63 = 21 HCF of x2 , x3 = x2 HCF of y,y2 =y HCF of z,z3 = z ∴ HCF = 21 x2 yz Question 5. 12ax2 ,6a2 x3 and 2a3 x5 Solution: 12ax2 , 6a2 x3 and 2a3 x5 HCF of 12, 6,2 = 2 HCF of a, a2 , a3 = a HCF of x2 , x3 , x5 = x2 ∴ HCF = 2ax2 Question 6. 9x2 , 15x2 y3 , 6xy2 and 21x2 y2 Solution: 9x2 , 15xV, 6xy2 and 21x2 y2
- 2. HCF of 9, 15, 6,21 = 3 HCF of x2 , x2 , x, x2 = x HCF of 1, y3 , y2 , y2 =2 ∴ HCF = 3x Question 7. 4a2 b3 -12a3 b, 18a4 b3 Solution: 4a2 b3 , -12a3 b, 18a4 b3 HCF of 4, 12, 18 = 2 HCF of a2 , a3 , a4 = a2 HCF of b3 ,b, b3 = b ∴ HCF = 2a2 b Question 8. 6x2 y2 , 9xy3 , 3x3 y2 Solution: 6x2 y2 , 9xy3 , 3x3 y2 HCF of 6, 9, 3 = 3 HCF of x2 , x, x3 = x HCF of y2 ,y3 ,y2 =y2 ∴ HCF = 3xy2 Question 9. a2 b3 , a3 b2 Solution: a2 b3 , a3 b2 HCF of a2 , a3 = a2 HCF of b3 , b2 = b2 ∴ HCF = a2 b2 Question 10. 36a2 b2 c4 , 54a5 c2 ,90a4 b2 c2 Solution: 36a2 b2 c4 , 54a5 c2 ,90a4 b2 c2 HCF of 36, 54, 90 = 18 HCF of a2 , a5 , a4 = a2 HCF of b2 , 1,b2 = 1 HCF of c4 ,c2 ,c2 = c2 ∴ HCF = 18a2 x 1 x c2 = 18a2 c2 Question 11. x3 , – yx2 Solution: x3 , – yx2 HCF of x3 , x2 = x2 HCF of 1, y= 1 ∴ HCF = x2
- 3. Question 12. 15a3 , -45a2 , -150a Solution: 15a3 ,-45a2 ,-150a HCF of 15,45, 150 = 15 HCF of a3 , a2 , a = a ∴ HCF = 15a Question 13. 2x3 y2 , 10x2 y3 , 14xy Solution: 2x3 y2 , 10x2 y3 , 14xy HCF of 2, 10, 14 = 2 HCF of x3 , x2 , x = x HCF of y2 ,y3 ,y=y ∴ HCF = 2xy Question 14. 14x3 y5 , 10x5 y3 , 2x2 y2 Solution: 14x3 y5 , 10x5 y3 , 2x2 y2 HCF of 14, 10, 2, = 2 HCF of x3 , x5 , x2 = x2 HCF of y5 ,y3 ,y2 =y2 ∴ HCF = 2xy Find the greatest common factor of the terms in each of the following expressions: Question 15. 5a4 + 10a3 – 15a2 Solution: 5a4 + 10a3 – 15a2 HCF of 5, 10, 15 = 5 HCF of a4 , a3 , a2 = a2 ∴ HCF = 5a2 Question 16. 2xyz + 3x2 y + 4y2 Solution: 2xyz + 3x2 y + 4y2 HCF of 2, 3,4 = 1 HCF of x, x2 , 1 = 1 HCF of y,y,y2 =y HCF of z, 1, 1 = 1 ∴ HCF = y
- 4. Question 17. 3a2 b2 + 4b2 c2 + 12a2 b2 c2 Solution: 3a2 b2 + 4b2 c2 + 12a2 b2 c2 HCF of 3, 4, 12 = 1 HCF of a2 , 1, a2 = 1 HCF of b2 , b2 , b2 = b2 HCF of 1, c2 , c2 = 1 ∴ HCF = b2