Question

x^4 + (2b^2-a^2) x^2+ b^4 with process please totally in need right now

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((x4) + ((2b2 - a2) • x2)) + b4

STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 2b2-a2

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 : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

((x4) + (2b2 - a2) • x2) + b4

STEP

3

:

Checking for a perfect cube

3.1 x4+2x2b2-x2a2+b4 is not a perfect cube

Final result :

x4 + 2x2b2 - x2a2 + b4