Question

try: multiply two binomials using foil
use the table below to foil \\((8x - 3)(x^2 + 1)\\).

term	expression	product
outer	\\(\boxed{}\\)	\\(8x\\)
inner	\\(-3 \cdot x^2\\)	\\(\boxed{}\\)
last	\\(\boxed{}\\)	\\(-3\\)

check
explain

Explanation:

Step1: Calculate First term

Multiply \(8x\) and \(x^2\). Using the rule of exponents \(a^m \cdot a^n = a^{m + n}\), we have \(8x\cdot x^{2}=8x^{1 + 2}=8x^{3}\).

Step2: Determine Outer term

In FOIL, Outer terms are the first term of the first binomial and the second term of the second binomial. So the Outer expression is \(8x\cdot1\).

Step3: Calculate Inner term

Multiply \(- 3\) and \(x^{2}\), we get \(-3\cdot x^{2}=-3x^{2}\).

Step4: Determine Last term

In FOIL, Last terms are the second term of the first binomial and the second term of the second binomial. So the Last expression is \(-3\cdot1\).

Answer:

First Product: \(8x^{3}\)
Outer Expression: \(8x\cdot1\)
Inner Product: \(-3x^{2}\)
Last Expression: \(-3\cdot1\)