(iv)(y^(2)+(3)/(2))(y^(2)-(3)/(2))

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Simplify : (i) (5x - 9y) - (-7x + y) (ii) (x^(2) -x) -(1)/(2)(x - 3 + 3x^(2)) (iii) [7 - 2x + 5y - (x -y)]-(5x + 3y -7) (iv) ((1)/(3)y^(2) - (4)/(7)y + 5) - ((2)/(7)y - (2)/(3)y^(2) + 2) - ((1)/(7)y - 3 + 2y^(2))

Add the following algebraic expressions: 2,(2y)/(3)-(5y^(2))/(3)+(5y^(3))/(2),-(4)/(3)+(2y^(2))/(3)-(y)/(2),(5y^(3))/(3)+3y^(2)+3y+(6)/(5)

If x=a^(2)cos^(3)theta and y=b^(2)sin^(3)theta then (i)(x^(2))/(a)+(y^(2))/(b)=1( ii) ((x)/(a^(2)))^((1)/(3))+((y)/(b^(2)))^((1)/(3))( iii) ((x^(2))/(a^(2)))^((2)/(3))+((y^(2))/(a^(2)))^((2)/(3))=1( iv) ((x)/(a^(2)))^((2)/(3))+((y)/(b^(2)))^((2)/(3))=1

Write the following squares of binomials as trinomials: (x+(x^(2))/(2))^(2) (ii) ((x)/(4)-(y)/(3))(3x-(1)/(3x))^(2)( iv )((x)/(y)-(y)/(x))^(2)

If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are vertices of equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2) then

If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2) then x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=

Simplify: ((1)/(3)y^(2)-(4)/(7)y+11)-((1)/(7)y-3+2y^(2))-((2)/(7)y-(2)/(3)y^(2)+2)