The LCM of 6(x^2 + xy), 8(xy - y^2), 12(x^2 - y^2) and (x + y)^2 is :

Question

The LCM of \(6(x^2 + xy),\) \(8(xy - y^2),\) \(12(x^2 - y^2)\) and 20\((x + y)^2\) is :

(a) 120x (x + y)(x - y)

(b) 120xy (x + y)(x - y)

(c) 120xy (x + y)²(x - y)

(d) 120xy (x + y)(x - y)²

Answer 1

(d) 120 xy (x - y)(x + y)²

6(x² + xy) = 6x(x + y)

8(xy - y²) = xy(x - y)

12(x² - y²) = 12(x - y)(x + y)

20(x + y)² = 20(x + y)(x + y)

LCM of 6, 8, 12, 20 = 120

∴ Reqd. LCM = 120 xy (x - y)(x + y)²