If a polynomial expression is in the form
(x)2+2(x)(y)+(y)2,then it is equivalent to
(x+y)2.Because
9a4+12a2b2+4b4=(3a2)2+2(3a2)(2b2)+(2b2)2
,it cab be re written as
(3a2+2b2)2 Choice B is incorrect. The expression
(3a+2b2)2 is equivalent to the product
(3a+2b)(3a+2b)(3a+2b)(3a+2b).This product will contain the term
4(3a)3(2b)=216a3b.However, the given polynomial,
9a4+12a2b2+4b4 does not contain the term
216a3b.Therefore,
9a4+12a2b2+4b4≠(3a+2b)4
.Choice C is incorrect. The expression
(9a2+4b2).This product will contain the terms
(9a2)(9a2)=81a4.However, the given polynomial,
9a4+12a2b2+4b4 does not contain the term
81a4,Therefore
9a4+12a2b2+4b4≠(9a2+4b2)2Choice D is incorrect. The expression
(9a+4b)4 is equivalent to the product
(9a+4b)(9a+4b)(9a+4b)(9a+4b) This product will contain the term
(9a)(9a)(9a)(9a)=6,561a4.However, the given polynomial,
9a4+12a2b2+4b4, does not contain the term
6,561a4 Therefore,
9a4+12a2b2+4b4≠(9a+4b)4