Answer:
(5x + 1) • (5x - 1)
Explanation:
Step 1:
Equation at the end of step 1:
5^2x^2 - 1
Step 2:
Trying to factor as a Difference of Squares :
Factoring: 25x^2-1
Theory :
A difference of two perfect squares,
A difference of two perfect squares, A^2 - B^2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B)
= A^2 - AB + BA - B^2
= A^2 - AB + AB - B^2
= A^2 - B^2
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 : 1 is the square of 1
Check : x^2 is the square of x^1
Factorization is :
(5x + 1) • (5x - 1)
Final result :
(5x + 1) • (5x - 1)