Question

How do you simplify `12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)`?

Answer 1

`9a^3 +13ab +4b^3`

Explanation:

Step one : Expand the brackets

`12a(a^2+ b) - 5b(b^2+a) + 9b(b^2 + a) - 3a(a^2 +b) =`

`(12a)(a^2) + (12a)(b) (-5b)(b^2)+(-5b)(a)+(9b)(b^2)+(9b)(a)(-3a)(a^2)+(-3a)(b) =`
which gives us

`12a^3+12ab-5b^3-5ab+9b^3+9ab-3a^3-3ab`

Step two : Collect like terms

1. #color(red)(12a^3)-5b^3-5ab+9b^3+9ab color(red)( -3a^3)-3ab= color(green)(9a^3)-5b^3-5ab+9b^3+9ab-3ab#
2. `9a^3+color(red)(12ab)-5b^3color(red)(-5ab)+9b^3color(red)(+9ab) color(red)(-3ab) = 9a^3 + color(green)(13ab)-5b^3+9b^3`
3. `9a^3+13abcolor(red)(-5b^3)+color(red)(9b^3)= 9a^3 +13ab +color(green)(4b^3)`

Answer:
`9a^3 +13ab +4b^3`