2x^4=50 factor and simplify all irrational and complex solutions

2x4 - 50

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x4 - 50 = 2 • (x4 - 25)

Trying to factor as a Difference of Squares:

3.2 Factoring: x4 - 25

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 : 25 is the square of 5

Check : x4 is the square of x2

Factorization is : (x2 + 5) • (x2 - 5)

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.