Jasonbradley
Home

(xy+1)(x+1)(y+1)+xy 因数分解

3 min read Jun 17, 2024
(xy+1)(x+1)(y+1)+xy 因数分解

Factoring the Expression (xy+1)(x+1)(y+1)+xy

The expression (xy+1)(x+1)(y+1)+xy can be factored into a simpler form. Here's how to do it:

  1. Expand the expression:
  • Start by expanding the first part of the expression: (xy+1)(x+1)(y+1) = (x^2y + xy + x + 1)(y+1)
  • Then, multiply the result by (y+1): x^2y^2 + x^2y + xy^2 + xy + xy + x + y + 1.
  • Now we have the complete expanded expression: x^2y^2 + x^2y + xy^2 + 2xy + x + y + 1 + xy.
  1. Rearrange the terms:
  • Group the terms that have common factors: (x^2y^2 + xy^2) + (x^2y + 2xy + x) + (y + 1).
  1. Factor out common factors:
  • From the first group, factor out xy^2: xy^2(x+1).
  • From the second group, factor out x: x(xy + 2y + 1).
  • The third group remains as it is: (y+1).
  1. Combine the factored terms:
  • The expression now looks like this: xy^2(x+1) + x(xy + 2y + 1) + (y+1).
  • Notice that the term (x+1) appears in the first term and the term (y+1) appears in the third term.
  1. Factor by grouping:
  • Group the first and third terms: [xy^2(x+1) + (y+1)] + x(xy + 2y + 1)
  • Factor out (x+1) from the first group and x from the second group: (x+1)(xy^2+1) + x(xy+2y+1)
  1. Final factorization:
  • We can see that (xy+1) is a common factor in both terms.
  • Factor out (xy+1): (xy+1)(x+1+x(y+1))

Therefore, the factored form of the expression (xy+1)(x+1)(y+1)+xy is (xy+1)(x+1+x(y+1)).

Related Post

Featured Posts