If (3a+4b)=16 and ab=4. Find (9a^2+16b^2)

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) 

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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)?

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