(" iv ")(4ab^(2)(-5ab^(3)))/(10a^(2)b^(2))

Simplify that: (4ab^(2)(-5ab^(3)))/(10a^(2)b^(2))

tan (i log ((a-ib)/(a+ib))) = (i) ab (ii) (2ab)/(a^(2) -b^(2)) (iii) (a^( 2) -b^(2))/(ab) (iv) (2ab)/(a^(2)+b^(2))

If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

Simplify: a^(2)b(a-b^(2))+ab^(2)(4ab-2a^(2))-a^(3)b(1-2b)

If a:b=2:3, then the value of (5a^(3)-2a^(2)b):(3ab^(2)-b^(3)) is :

Add : 3ab^(2) , - 5ab^(2)

Prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

Simplify : 6a^(2)+3ab+5b^(2)-2ab-b^(2)+2a^(2)+4ab+2b^(2)-a^(2) .

Multiply: (i) 6ab by 4b (ii) 5ab^(2)c^(3) by 7a^(2)bc (iii) -6x^(2)yz by (2)/(3)xy^(3)z^(2) (iv) (-8)/(5)a^(2)bc^(3) by (-3)/(4)ab^(2)c

Simplify: 4ab(a-b)-6a^(2)(b-b^(2))-3b^(2)(2a^(2)-a)+2ab(b-a)