" 30."a(a-2b-c)+2bc

Factorise : a(a-2b-c)+2bc

If (a-2b-3c+4d)(a+2b+3c+4d) = (a+2b-3c-4d)(a-2b+3c-4d) then 2ad = "(a) 3bc (b) bc (c) 5bc (d) 2bc"

Evaluate : (ix) (a+ bc ) (a- bc) (a^2 + b^2 c^2)

Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a b,-a b)|=(a b+b c+c a)^3

Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a b,-a b)|=(a b+b c+c a)^3

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))

Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

|[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|=|[a,b,c],[b,c,a],[c,a,b]|^2

Evaluate : (vi) (a + bc ) ( a- bc ) (a^2 + b^2 c^2)