Question

Factorise the following expression :​

Answer 1

`ii)(x^2+5)(x+2)\\iv)(a^2-b)(a-b^2)`

Explanation:

`ii)We\ are\ given,\\x^3+2x^2+5x+10\\Let's\ separate\ the\ terms\ the\ terms\ using\ the\ Associative\ Property\ Of\\ Addition:\\(x^3+2x^2)+(5x+10)\\=(x*x^2+2*x^2)+5*x+5*2\\=x^2(x+2)+5(x+2) [Taking\ out\ (x+2)\ from\ each\ term]\\=(x^2+5)(x+2) [Using\ the\ Distributive\ Property\ to\ re-combine\ the\ terms]`

`iv)We\ are\ given,\\a^3-a^2b^2-ab+b^3\\Lets\ again\ separate\ the\ terms\ using\ the\ Associative\ Property\ Of\\ Addition:\\(a^3-a^2b^2)+(-ab+b^3)\\=a^2(a-b^2)+(b(-a+b^2))\\Now,\\Here,\\We\ cannot\ directly\ apply\ Distributive\ Property\ as:\\a-b^2\\eq -a+b^2\\Rather,\ just\ represent\ 1b\ in\ the\ second\ term\ as:\\-1*-1*b\\Hence,\\a^3-a^2b^2-ab+b^3\\=a^2(a-b^2)+(b(-a+b^2))\\=a^2(a-b^2)+(-1*b*-1(-a+b^2))\\=a^2(a-b^2)-b(a-b^2)\\=(a^2-b)(a-b^2)\ [Re-grouping\ the\ terms\ using\ Distributive\ Property]`

Answer 2

x³+2x²+5x+10

x²(x+2)+5(x+2)

(x+2)(x²+5)

a³-a²b²-ab+b³

a²(a-b²)-b(a-b²)

(a-b²)(a²-b)