Question

Factor the expression 36s^2-25

Answer 1

Answer:

(6x + 5) • (6x - 5)

Step-by-step explanation:

36x2-25

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22•32x2) -  25

Step  2  :

Trying to factor as a Difference of Squares :

2.1      Factoring:  36x2-25

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 :  36  is the square of  6

Check : 25 is the square of 5

Check :  x2  is the square of  x1

Factorization is :       (6x + 5)  •  (6x - 5)

Final result :

 (6x + 5) • (6x - 5)