Question

Which of the following is equivalent to x4 - y4? Select all that apply.

Answer 1

Answer: (x^2-y^2) (x^2+y^2)  and  (x-y)(x+y)(x^2+y^2)

Step-by-step explanation:

(x2  − y2) (x2  + y2)  

Expand (x2 − y2) (x2 + y2) using the FOIL Method.

Apply the distributive property.

x^2 (x^2 + y^2 ) − y^2 (x^2 + y )

Apply the distributive property.

x^2 x^2 +x^2 y^2 - y^2 (x^2 y^2 )

Apply the distributive property.

x^2 x^2 + x^2 y^2 - y^2 x^2- y^2 y^2

Combine the opposite terms in x^2 x^2 + x^2  y^2 - y^2  x^2 - y^2 y^2.

Reorder the factors in the terms x^2 y^2 and − x^2 y^2.

x^2 x^2+ x^2 y^2 - x^2 y^2 - y^2 y^2

Subtract 2 2 from 2 2.

x^2 x^2+ 0 - y^2 y^2

Add 2  2 and 0.

x2 x2- y2 y2

Simplify each term.

Multiply x2 by x2 by adding the exponents.

x^4 − y^2y^2

x^4 − y^4

(x-y)(x+y)(x^2+y^2)

(x − y) (x + y) (x^2 + y^2)

Expand (x − y) (x + y) using the FOIL Method.

(x ⋅ x + xy − yx − y ⋅ y) (x^2 + y^2)

Combine the opposite terms in x ⋅ x + xy − yx − y ⋅ y.

(x ⋅ x − y ⋅ y) (x^2 + y^2)

(x^2 − y^2) (x^2 + y^2)

Expand (x^2 − y^2) (x^2 + y^2) using the FOIL Method.

Apply the distributive property.

x^2 (x^2 + y^2) − y^2 (x^2 + y^2)

Apply the distributive property.

x^2 x^2 + x^2y^2 - y^2 (x^2 + y^2)

Apply the distributive property.

x^2 x^2 + x^2 y^2 - y^2 x^2 - y^2 y ^2

Combine the opposite terms in x^2x^2 + x^2y^2 − y^2x^2 − y^2y^2.

x^2x^2 − y^2y^2

x^4 − y^4

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