Question

Factor the expression
36s^2-25

Answer 1

(6x + 5) • (6x - 5)

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)