" (vii) "(ax+by)^(2)-(bx+ay)^(2)

2 (ax+by)^(2)-(bx+ay)^(2)

(ax+by)^(2)-(ay+bx)^(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)

Factorise : (v) (ax + by )^(2) + (bx - ay)^(2)

The area of the equilaterial triangle formed by the pair of lines (ax+by)^(2)-3(bx-ay)^(2)=0 and the line ax+by+c=0 is (c^(2))/(sqrt(3)(a^(2)+b^(2))) sq. units.

Fractorise: (ax + by) ^(2) + (bx - ay)^(2)

Show that pair of bisectors of angles between the lines (ax + by)^(2) = c(bx - ay)^(2) (c gt 0) are parallel and perpendicular to the line ax+by+k=0

Ifx=a sin theta+b cos theta,y=a cos theta-b sin theta then show that (ax+by)^(2)+(bx-ay)^(2)=(a^(2)+b^(2))^(2)

If x=a sin theta+b cos theta,y=a cos theta-b sin theta then show that (ax+by)^(2)+(bx-ay)^(2)=(a^(2)+b^(2))^(2)

Factorise: ax ^(2) + by^(2) + bx^(2) + ay^(2)