Factor the expression 25x2 – 1.

(5x + 1) • (5x - 1)

Step-by-step 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)

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