Question

Expand and combine like terms. (4b^2+3)(4b^2-3)

Answer 1

Answer:

16b^4-9

Step-by-step explanation:

Factoring gives us 16b^4+12b^2-12^2-9. Simplifying gives us the answer which is 16b^4-9

Answer 2

Answer:

$16b^4-9$

Step-by-step explanation:

When multiplying binomials, we can use a method called FOIL (First-Outside-Inside-Last).

For $(t_1+t_2)(t_3+t_4)$, let:

$t_1\implies \text{First Term},\\t_2\implies \text{Second Term},\\t_3\implies \text{Third Term},\\t_4\implies \text{Fourth Term}$

In the FOIL method, the steps go:

$\text{\textbf{F}irst: Multiply the first and third terms (first term of each binomial)},\\\text{\textbf{O}utside: Multiply the first and fourth terms},\\\text{\textbf{I}nside: Multiply the second and third terms},\\\text{\textbf{L}ast: Multiply the second and fourth terms (last term of each binomial) }$

Given $(4b^2+3)(4b^2-3)$, we have:

$\text{First: }4b^2\cdot 4b^2,\\\text{Outside: }4b^2\cdot -3,\\\text{Inside: }3\cdot 4b^2,\\\text{Last: }3\cdot -3,\\\rightarrow 16b^4-12b^2+12b^2-9$

Combine like terms:

$\boxed{16b^4-9}$