How do you simplify 12a (a^2 + b) - 5b (b^2 + a) + 9b (b^2 + a) - 3a (a^2 + b)12a(a2+b)5b(b2+a)+9b(b2+a)3a(a2+b)?

1 Answer
Sep 20, 2017

9a^3 +13ab +4b^39a3+13ab+4b3

Explanation:

Step one : Expand the brackets

12a(a^2+ b) - 5b(b^2+a) + 9b(b^2 + a) - 3a(a^2 +b) =12a(a2+b)5b(b2+a)+9b(b2+a)3a(a2+b)=

(12a)(a^2) + (12a)(b) (-5b)(b^2)+(-5b)(a)+(9b)(b^2)+(9b)(a)(-3a)(a^2)+(-3a)(b) =(12a)(a2)+(12a)(b)(5b)(b2)+(5b)(a)+(9b)(b2)+(9b)(a)(3a)(a2)+(3a)(b)=
which gives us

12a^3+12ab-5b^3-5ab+9b^3+9ab-3a^3-3ab12a3+12ab5b35ab+9b3+9ab3a33ab

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-3ab12a35b35ab+9b3+9ab3a33ab=9a35b35ab+9b3+9ab3ab
  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^39a3+12ab5b35ab+9b3+9ab3ab=9a3+13ab5b3+9b3
  3. 9a^3+13abcolor(red)(-5b^3)+color(red)(9b^3)= 9a^3 +13ab +color(green)(4b^3)9a3+13ab5b3+9b3=9a3+13ab+4b3

Answer:
9a^3 +13ab +4b^39a3+13ab+4b3