Using `a^2-b^2`=`(a+b)(a-b) find `12.1^2-7.9^2`

Using a^2-b^2 = (a+b)(a-b) find 153^2-147^2

Using a^2-b^2 = (a+b)(a-b) find (1.02)^2-(0.98)^2

Using a^2-b^2 = (a+b)(a-b) 'find' 51^2-49^2

Using (x+a)(x+b) = x^2+(a+b)x+ab find 9.7 xx9.8

Using (x+a)(x+b) = x^2+(a+b)x+ab find 5.1 xx 5.2

a) Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx" and evaluate "int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) b) Prove that |{:(1+a^(2)-b^(2), 2ab, -2b), (2ab, 1-a^(2)+b^(2), 2a), (2, -2a, 1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)

Factorise each of the following : (i) 8a^3+b^3+12a^2b+6ab^2 (ii) 8a^3-b^3-12a^2b+6ab^2 (iii) 27-125a^3-135a+225a^2 (iv) 64a^3-27b^3-144a^2b+108ab^2 (v) 27p^3-1/(216)-9/2p^2+1/4p s

Use the identity (x+a)(x+b) = x^2+(a+b)x +ab to find the following products (2a^2+9)(2a^2+5)

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

If a =2, b=-2, find the value of : a^2-b^2