Question

resolve into factor 9a^2b^4-16​

Answer 1

Answer:

(3ab2 + 4) • (3ab2 - 4)

Step-by-step explanation:

STEP1:Equation at the end of step 1 (32a2 • b4) - 16 STEP2:Trying to factor as a Difference of Squares:

 2.1      Factoring:  9a2b4-16 

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 :  b4  is the square of  b2 

Factorization is :       (3ab2 + 4)  •  (3ab2 - 4) 

Trying to factor as a Difference of Squares:

 2.2      Factoring:  3ab2 - 4 

Check :  3  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Final result :

(3ab2 + 4) • (3ab2 - 4)

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