[xy(a^(2)+b^(2))," 20."a^(2)+ab(b+1)+b^(3)],[-2b^(2)," 22."(ax+by)^(2)+(bx-ay)^(2)]

Factorise the following expressions : (i) ax-ay+bx-by " " (ii) x^(2)-x-ax+a " " (iii) x^(4)+x^(3)+x^(2)+x (iv) 16(a+b)^(2)-4a-4b " " (v) x^(2)+(1)/(x^(2))+2-3x-(3)/(x) " " (vi) x^(2)-((a)/(b)+(b)/(a))x+1 (vii) x^(2)+(a-(1)/(a))x-1 " " (viii)ab(x^(2)+y^(2)+xy(a^(2)+b^(2)) " "(ix) (ax+by)^(2)+(bx-ay)^(2)

Factorize each of the following expressions: x^(2)-2ax-2ba+bx(2)x^(3)-2x^(2)y+3xy^(2)-6y^(3)abx^(2)+(ay-b)x-y(4)(ac+by)^(2)+(bx-ay)^(2)

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 tangent of the angle between the lines whose intercepts on the axes are respectively a ,-b and b ,-a ............... A) tan ^(-1)""(a^(2) +b^(2))/(ab) B) tan ^(-1)""(b ^(2) -a^(2))/(2) C) tan ^(-1)""(b^(2) -a^(2))/(2ab) D) tan ^(-1)""(b^(2) -a^(2))/(ab)

Factorise the using the identity a ^(2) + 2 ab + b ^(2) = (a + b) ^(2) a ^(2) x ^(2) + 2 ab xy + b ^(2) y ^(2)

6(ax+by)=3a+2b&6(bx-ay)=3b-2a

prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),,(b-z)^(2)),((c-x)^(2),,(c-y)^(2),,(c-z)^(2)):}| |{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}| =2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)

Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)

Show that |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|=(1+a^(2)+b^(2))^(3)