Question

Factor x^4+xy^3+x^3+y^3 out completely. Hint: first factor out a monomial.

Answer 1

Answer:

(x + y)(x² - xy + y²)(x + 1)

Step-by-step explanation:

Given

$x^{4}$ + xy³ + x³ + y³ ( factor out x from the first 2 terms )

= x(x³ + y³) + 1(x³ + y³) ← factor out (x³ + y³) from each term

= (x³ + y³)(x + 1)

x³ + y³ is a sum of cubes and factors as (x + y)(x² - xy + y²)

Thus

$x^{4}$ + xy³ + x³ + y³ = (x + y)(x² - xy + y²)(x + 1)