Which expression is equivalent to (x4) - 5

(x2 + y2) • (x + y) • (x - y)

Step-by-step explanation:

Trying to factor as a Difference of Squares:

1.1 Factoring: x4-y4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : x4 is the square of x2

Check : y4 is the square of y2

Factorization is : (x2 + y2) • (x2 - y2)

Trying to factor as a Difference of Squares:

1.2 Factoring: x2 - y2

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + y) • (x - y)

Final result:

(x2 + y2) • (x + y) • (x - y)