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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