Formulae for the sum and differences of cubes `(i) a^3 +b^3 = (a+b)(a^2-ab+b^2) (ii) a^3-b^3 = (a-b)(a^2+ab+b^2)`

If a+b=4 and a^3+ b^3=8 , then a^2-ab+b^2

a^3 - b^3 - 3a^2b+ 3ab^2, by, a^2 + b^2 - 2ab

(a^3-b^3)/(a^2+b^2+ab)=

(a ^ (2) -b ^ (2)) / (ab) - (a ^ (3) -b ^ (3)) / (a ^ (2) -b ^ (2))

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

(ii) If a-b=3 and a^2 + b^2 = 29 , find ab .

If a = 2 and b = 3, find the value of (i) a + b (ii) a^(2) + ab (iii) ab - a^(2) (iv) 2a - 3b (v) 5a^(2) - 2ab (vi) a^(3) - b^(3)

Factorise the difference: (i)3-12(a-b)^(2)(ii)1-2ab-(a^(2)+b^(2))