*f.2 mathz

1. 6ab3, 8a2bc, 12bc2

= 2 X 3ab3, 23a2bc, 22 X 3bc2

H.C.F. = 2b

L.C.M. = 23 X 3a2b3c2 = 24a2b3c2


2. 4(a + b)(a + p) and 6(a + b)(a + q)

= 2 X 2(a + b)(a + p) and 2 X 3(a + b)(a + q)

H.C.F. = 2(a + b)

L.C.M. = 2 X 2 X 3(a + b)(a + p)(a + q)

= 12(a + b)(a + p)(a + q)


3. a2 + a and ab + a

= a(a + 1) and a(b + 1)

H.C.F. = a

L.C.M. = a(a + 1)(b + 1)


1. -1 + x – 3x2 + x4

When x = 2

The value is

-1 + 2 – 3(2)2 + 24

= 5

2. –x – 3/2 + 1/2x3

When x = 3

The value is

-3 – 3/2 + 1/2(3)3

= -35/8

3. –x2y2 + x3y – 4x4 + xy3 – 3y4

When x = -2, y = 3

The value is

-(-2)2(3)2 + (-2)3(3) – 4(-2)4 + (-2)(3)3 – 3(3)4

= -421

Find the H.C.F. and L.C.M. of the following:

(1)6ab^3,8a^2bc,12bc^2
HCF = 2b
LCM = 24a^2b^3c^2


(2)4(a+b)(a+p) and 6(a+b)(a+q)
HCF = 2(a+b)
LCM = 12(a+b)(a+p)(a+q)


(3)(a^2+a) and (ab+a)
a^2+a = a(a+1)
ab+a = a(b+1)
HCF = a
LCM = a(a+1)(b+1)

Find the value of the following:

(1)-1+x-3x^2+x^4 (x=2)
= -1+2-3(2)^2+(2)^4
= -1+2-3(4)+(16)
= 5


(2)-x-3/2+1/2x^3 (x=3)
As not sure the question,
If (-x-3)/2+1/(2x^3) (x=3)
= (-3-3)/2+1/[2(3)^3]
= -6/2+1/54
= -161/54
If -x-(3/2)+1/(2x^3) (x=3)
= -3-(3/2)+1/[2(3)^3]
= -3-3/2+1/54
= -242/54
= -121/27


(3)-x^2y^2+x^3y-4x^4+xy^3-3y^4 (x=-2,y=3)
= -(-2)^2(3)^2+(-2)^3(3)-4(-2)^4+(-2)(3)^3-3(3)^4
= -(4)(9)+(-8)(3)-4(16)+(-2)(27)-3(81)
= -36-24-64-54-243
= -421