The polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.
Polynomials are algebraic expressions that consist of variables and coefficients where arithmetic operations can be performed.
A polynomial is expanded if no variable appears within parentheses and all like terms have been combined.
To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations. Then combine all like terms.
Expanding each of the options provided using FOIL method:
a) (3x+2i)(3x-2i)
= 9x^2 - 2ix + 2ix - 4i^2
= 9x^2 - 4i^2 *(i^2 = -1) note that i is an imaginary number and i squared is equal to -1
= 9x^2 - 4(-1)
= 9x^2 + 4
b) (3x+2)(3x-2)
= 9x^2 + 6x - 6x - 4
= 9x^2 - 4
c) (3x + 2i)^2
= 9x^2 + 6ix + 6ix + 4i^2 *(i^2 = -1)
= 9x^2 + 12ix - 4
d) (3x + 2)^2
= 9x^2 + 6x + 6x + 4
= 9x^2 + 12x + 4
Hence, the polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.
To learn more about polynomials: brainly.com/question/1218464
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