What is the completely factored form of 25x4-16y2

25x4-16y2

Final result:

(5x2 + 4y) • (5x2 - 4y)

Reformatting the input:

Changes made to your input should not affect the solution:

(1) : "y2" was replaced by "y^2". 1 more similar replacement (s).

Step by step solution:

Step 1:

Equation at the end of step 1:

(25 • (x4)) - 24y2

Step 2:

Equation at the end of step 2:

52x4 - 24y2

Step 3:

Trying to factor as a Difference of Squares:

3.1 Factoring: 25x4-16y2

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 : 16 is the square of 4

Check : x4 is the square of x2

Check : y2 is the square of y1

Factorization is : (5x2 + 4y) • (5x2 - 4y)

Trying to factor as a Difference of Squares:

3.2 Factoring: 5x2 - 4y

Check : 5 is not a square!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Final result:

(5x2 + 4y) • (5x2 - 4y)

Step-by-step explanation: i looked it up and this is what i got sorry if its wrong