Question

rewrite the following expression in expanded form and simplify completely. $(x - y)^4$
check answer

Explanation:

Step1: Rewrite as repeated multiplication

$(x-y)^4 = (x-y)(x-y)(x-y)(x-y)$

Step2: Multiply first two binomials

$(x-y)(x-y) = x^2 - 2xy + y^2$

Step3: Multiply result by third binomial

$(x^2 - 2xy + y^2)(x-y) = x^3 - 3x^2y + 3xy^2 - y^3$

Step4: Multiply result by fourth binomial

$(x^3 - 3x^2y + 3xy^2 - y^3)(x-y) = x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4$

Answer:

$x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4$