`(1)/(8) a^(3) + (1)/(4) a^(2)b + (1)/(6) ab^(2) + (65)/(27)b^(3)` का गुणनखंड कीजिये।

Factorise: (1)/(64) a ^(3) - (1)/(16) a ^(2) b + (1)/(12) ab ^(2) - (1)/(27) b ^(3)

((1)/(216))^(-2/3)-:((1)/(27))^(-4/3)=? a.(3)/(4)b*(2)/(3) c.(4)/(9)d.(1)/(8)

Factorise each of the following : (i) 8a^(3)+b^(3)+12a^(2)b+6ab^(2) (ii) 8a^(3)-b^(3)-12a^(2)b+6ab^(2) (iii) 27-125a^(3)-135a+225a^(2) (iv) 64a^(3)-27b^(3)-144a^(2)b+108ab^(2) (v) 27p^(3)-(1)/(216)-(9)/(2)p^(2)+(1)/(4)p

Show that , if A = [{:(1,3),(2,6) :}] and B = [{:(-1,4), (2,1):}] then : (A +B) ^(2) ne A ^(2) + 2 AB + B ^(2).

8a^(3)-27b^(3)-1-18ab

If log_(4)5=a and log_(5)6=b, then log_(3)2 is equal to (1)/(2a+1) (b) (1)/(2b+1)(c)2ab+1(d)(1)/(2ab-1)

The factors of 8a^(3)+b^(3)-6ab+1 are (a) (2a+b-1)(4a^(2)+b^(2)+1-3ab-2a) (b) (2a-b+1)(4a^(2)+b^(2)-4ab+1-2a+b)(2a+b+1)(4a^(2)+b^(2)+1-2ab-b-2a) (d) (2a-1+b)(4a^(2)+1-4a-b-2ab)

If (a)/(b)=(1)/(3),backslash(b)/(c)=2,backslash(c)/(d)=(1)/(2),backslash(d)/(e)=3 and (e)/(f)=(1)/(4), then what is the value of (abc)/(def)?(1)/(4) (b) (3)/(4)(c)(3)/(8)(d)(27)/(4) (e) (27)/(8)

Verify that (AB)^(T) = B^(T) A^(T) if A = ({:( 2 , 3 , -1) , (4 , 1 , 5):}) and B = ({:( 1 , 2) , ( 3 , -3) , (2 , 6)):}