Question

Factorise the following:(a^2-1)(b^2-1)-4ab

Answer 1

Answer:

Step-by-step explanation:

a2-1)(b2-1)-4ab  

Final result :

 a2b2 - a2 - 4ab - b2 + 1

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

1.1      Factoring:  a2-1  

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 :  a2  is the square of  a1  

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

Trying to factor as a Difference of Squares :

1.2      Factoring:  b2 - 1  

Check : 1 is the square of 1

Check :  b2  is the square of  b1  

Factorization is :       (b + 1)  •  (b - 1)  

Equation at the end of step  1  :

 (a+1)•(a-1)•(b+1)•(b-1)-4ab

Step  2  :

Final result :

 a2b2 - a2 - 4ab - b2 + 1