Question

Find the HCF of 36 x^3 y^2 and 24x^4y^2
1) 12x^3y^2
2) 12x^4y^2
3) 24x^3y^2
4) 36x^4y^2

Answer 1

Answer:

Explanation:

Solution:

2x + 6 = 2 (x + 3)

x2 + 3x = x (x + 3)

LCM = 2x (x + 3)

(ii) x2y + xy2, x 2+ xy

Solution:

x2y + xy2 = xy (x + y)

x 2+ xy = x ( x+ y)

LCM = xy (x + y)

(iii) 3x2 – 75, 2x3 + 250

Solution:

3x2 – 75 = 3 (x2 – 25)

= 3 (x2 – 52)

= 3 (x + 5) (x – 5)

2x3 + 250 = 2 (x3 + 125)

LCM = 2 x 3 (x + 5) (x3 + 125)

= 6 (x + 5) (x3 + 125)

(iv) a2 – 1, a4 – 1, a8 – 1

Solution:

a2 – 1 = (a + 1) (a – 1)

a4 – 1 = (a2 + 1) (a2 – 1)

= (a2 + 1) (a + 1) (a – 1)

a8 – 1 = (a4 + 1) (a4 – 1)

= (a4 + 1) [(a2)2 – 12]

= (a4 + 1) (a2 + 1) (a2 – 1)

= (a4 + 1) (a2 + 1) (a + 1) (a – 1)

LCM = (a + 1) (a – 1) (a2 + 1) (a4 + 1)

(v) m2 – n2 , 3m2 – 3mn

Solution:

m2 – n2 = (m + n) (m – n)

3m2 – 3mn = 3m (m – n)

LCM = 3m (m + n) (m – n)

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