Question

factorize -9a^2 -16b^2

Answer 1

Final result :

(3a + 4b) • (3a - 4b)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(9 • (a2)) - 24b2

Step  2  :

Equation at the end of step  2  :

32a2 - 24b2

Step  3  :

Trying to factor as a Difference of Squares :

 3.1      Factoring:  9a2-16b2 

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 :  9  is the square of  3 

Check : 16 is the square of 4

Check :  a2  is the square of  a1 

Check :  b2  is the square of  b1 

Factorization is :       (3a + 4b)  •  (3a - 4b) 

Final result :

(3a + 4b) • (3a - 4b)