[" (b) "x(2+5x)+10x^(2)-5x(2x-3)],[" (iii) "(a^(2))/(1)b(a-b^(2))+ab^(2)(4ab-2a^(2))-a^(3)b(1-2b)]

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

Find the product : (i) (x+3)(x^(2)-3x+9) " " (ii) (7+5b)(49-35b+25b^(2)) (iii) (5a+(1)/(2)) (25a^(2)-(5a)/(2)+(1)/(4)) " " (iv) (a+b-2)[a^(2)+b^(2)+4(a+b)+4] .

Compute the following: [(a,b),(-b,a)]+[(a,b),(b,a)] (ii) [(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2))]+[(2ab,2bc),(-2ac,-2ab)] (iii) [(-1,4,-6),(8,5,16),(2,8,5)]+[(12,7,6),(8,0,5),(3,2,4)] (iv) [(cos^(2)x, sin^(2)x),(sin^(2)x, cos^(2)x)]+[(sin^(2)x, cos^(2)x),(cos^(2)x, sin^(2)x)]

Compute the following: [(a,b),(-b,a)]+[(a,b),(b,a)] (ii) [(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2))]+[(2ab,2bc),(-2ac,-2ab)] (iii) [(-1,4,-6),(8,5,16),(2,8,5)]+[(12,7,6),(8,0,5),(3,2,4)] (iv) [(cos^(2)x, sin^(2)x),(sin^(2)x, cos^(2)x)]+[(sin^(2)x, cos^(2)x),(cos^(2)x, sin^(2)x)]

Compute the following: (i) [(a,b),(-b,a)]+[(a,b),(b,a)] (ii) [(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2))]+[(2ab,2bc),(-2ac,-2ab)] (iii) [(-1,4,-6),(8,5,16),(2,8,5)]+[(12,7,6),(8,0,5),(3,2,4)] (iv) [(cos^(2)x, sin^(2)x),(sin^(2)x, cos^(2)x)]+[(sin^(2)x, cos^(2)x),(cos^(2)x, sin^(2)x)]

a^(2)b^(3)x2ab^(2) is equal to: 2a^(3)b^(4)(b)2a^(3)b^(5)(c)2ab (d) a^(3)b^(5)

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is