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

$$(z^2 + 4)(z + 2)(z - 2)$$
To factor the difference of two squares, we use the formula: $$A^2 - B^2 = (A + B)(A - B)$$ For this binomial, we take the square root of the leading term $(z^4)$ to get $A = z^2$ and the square root of the second term $(16)$ to get $B = 4$. So we now plug these two values into the formula for factoring the binomial: $$(z^2 + 4)(z^2 - 4)$$ The second binomial is also a difference of two squares, so we can use the same formula to further factor this problem: To factor the difference of two squares, we use the formula: $$A^2 - B^2 = (A + B)(A - B)$$ For this binomial, we take the square root of the leading term $(z^2)$ to get $A = z$ and the square root of the second term $(4)$ to get $B = 2$. We plug these values into the equation to factor the difference of two squares to get: $$(z + 2)(z - 2)$$ We now add what we just factored to replace the binomial $(z^2 - 4)$ to get the final factorization of the original binomial: $$(z^2 + 4)(z + 2)(z - 2)$$