Question

Find the lcm of (2x^2-8) (3x^2-9x+6) and (6x^2+18x+12)

Answer 1

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)

(vi) 5(y2 – z2), y2 + 2yz + z2

Solution:

5(y2 – z2) = 5 (y – z) (y + z)

y2 + 2yz + z2 = (y + z)2 [(a + b)2 = a2 + 2ab + b2]

LCM = 5 (y – z) (y + z)2

(vii) x3 + 8, x2 – 4

Solution:

x3 + 8 = x3 + 23

= (x + 2) (x2 – 2x +4)

x2 – 4 = x2 + 22

= (x + 2) (x – 2)

LCM = (x + 2) (x – 2) (x2 – 2x +4) = (x+2)(x3+8)

(viii) 3(a + b)2, 5(a – b )2, 2(a2 – b2)

Solution:

3(a + b)2 = 3(a + b) (a + b)

5(a – b)2 = 5(a – b ) (a – b)

2(a2 – b2) = 2(a + b) (a – b)

LCM = 2 x 3 x 5 (a + b)2 (a – b)2

LCM =30 (a + b)2 (a – b)2 = 30(a2-b2)2