Question

Evaluate each of the following using identities.
(a²b²-d²)²
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Answer 1

1 result(s) found

(ab+d)  2  ⋅ (ab−d)  2

 

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Step by Step Solution:

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STEP

1

:

Trying to factor as a Difference of Squares:

1.1      Factoring:  a2b2-d2  

Put the exponent aside, try to factor  a2b2-d2  

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 :  a2  is the square of  a1  

Check :  b2  is the square of  b1  

Check :  d2  is the square of  d1  

Factorization is :       (ab + d)  •  (ab - d)  

Raise to the exponent which was put aside

Factorization becomes :   (ab + d)2   •  (ab - d)2  

Final result :

 (ab + d)2 • (ab - d)2