resolve into factor 9a^2b^4-16
Answers
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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