Question

Factorie:x⁸-y⁸

Answer 1

Trying to factor as a Difference of Squares :

1 Factoring: x⁸-y⁸

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 : x⁸ is the square of x⁴

Check : y⁸ is the square of y⁴

Factorization is :
(x⁴ + y⁴) • (x⁴ - y⁴)

Trying to factor as a Difference of Squares :

Factoring: x⁴ - y⁴

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 :

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 : (x⁴ + y⁴) • (x² + y²) • (x + y) • (x - y)