Question

Find the factors of : 25a square − 49

Answer 1

Answer:

.1      Factoring:  25a2-49  

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 : 49 is the square of 7

Check :  a2  is the square of  a1  

Factorization is :       (5a + 7)  •  (5a - 7)  

Final result :

 (5a + 7) • (5a - 7)

Step-by-step explanation: