Question

Expand and combine like terms.

(4b^2+3)(4b^2-3)

Answer 1

16b^4-9

Explanation:

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

Answer 2

`16b^4-9`

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}`