Question

(x4 – 4a4) = (x - a)​

Answer 1

Step-by-step explanation:

Step 1 :

x4 - a4

Simplify ———————

x - a

Trying to factor as a Difference of Squares :

1.1 Factoring: x4 - a4

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 : a4 is the square of a2

Factorization is : (x2 + a2) • (x2 - a2)

Trying to factor as a Difference of Squares :

1.2 Factoring: x2 - a2

Check : x2 is the square of x1

Check : a2 is the square of a1

Factorization is : (x + a) • (x - a)

Canceling Out :

1.3 Cancel out (x - a) which appears on both sides of the fraction line.

Final result :

(x2 + a2) • (x + a)