Question

Find the factors of 1-81a2

Answer 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

1 - 34a2

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  1-81a2 

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 :  1  is the square of  1 
Check : 81 is the square of 9
Check :  a2  is the square of  a1 

Factorization is :       (1 + 9a)  •  (1 - 9a) 

Final result :

(9a + 1) • (1 - 9a)

Answer 2

Answer:

(1 + 9a) (1 - 9a)

Step-by-step explanation:

 1 - 81a²

= 1² - (9a)²    [ ∵ 1² = 1 and (9a)² = 81a²]

Using Identity a² - b² = (a + b) (a - b), where a = 1 and b = 9a

= (1 + 9a) (1 - 9a)