how do i factor this problem?

Comments

• big-fat-greek-guy

  May 2021

  Simple!

  Factoring is based on polynomials (I.E. quantities connected through multiplication or division)

  So we have (8z-3)(z+8) - (8z-3)(z-7) where

  (8z-3) and (z+8) are connected through multiplication

  and

  (8z-3) and (z-7) is also connected through multiplication

  Now we look for what the two terms have in common.

  Since both polynomials have (8z-3) we can factor it out.

  Factoring is basically the opposite of distributing...

  When we have something like:

  x(y+z)

  we can make that xy+xz

  So to factor this problem... just do the opposite:

  (8z-3)(z+8) - (8z-3)(z-7)

  Both have (8z-3) so pull it out.

  Factored answer: (8z-3)((z+8)-(z-7))

  We could keep going by taking care of the terms connected through subtraction...

  (8z-3)((z+8)-(z-7))

  becomes

  (8z-3)(z+8-z+7)

  then

  (8z-3)(15)

  and finally

  Simplified answer: 120z-45

  Factored answer: (8z-3)((z+8)-(z-7))