## Introductory Algebra for College Students (7th Edition)

$$x^4 + 6x^2 + 9$$
First, let us expand the expression to be able to clearly see the terms: $$(x^2 + 3)(x^2 + 3)$$ Use the distributive property to multiply each term in the binomial by each term in the second binomial: $$(x^2)(x^2) + (x^2)(3) + (3)(x^2) + (3)(3)$$ Multiply the coefficients and add exponents according to the product rule for exponents, which states that if the bases of two monomials are the same, we can add the exponents and keep the variable: $$x^{2 + 2} + 3x^2 + 3x^2 + 9$$ Simplify by adding the exponents: $$x^4 + 3x^2 + 3x^2 + 9$$ Group like terms: $$x^4 + (3x^2 + 3x^2) + 9$$ Combine like terms: $$x^4 + 6x^2 + 9$$