Question

try it!
try: multiply two terms
when multiplying $3x$ and $2x^2$, we add/multiply the coefficients of the terms and add/multiply the exponents of $x$.
$(3x)(2x^2)=\square$
check
explain

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

term	expression	product
outer	$\square$	$8x$
inner	$-3 \cdot x^2$	$\square$
last	$\square$	$-3$

check
explain

Explanation:

Part 1: Multiplying \(3x\) and \(2x^2\)

Step1: Determine coefficient operation

To multiply \(3x\) and \(2x^2\), we multiply the coefficients (3 and 2) and add the exponents of \(x\) (1 and 2, since \(x = x^1\)).

Step2: Multiply coefficients

Multiply the coefficients: \(3\times2 = 6\).

Step3: Add exponents of \(x\)

Add the exponents of \(x\): \(x^1\times x^2=x^{1 + 2}=x^3\).

Step4: Combine results

Combine the coefficient and the variable part: \(6x^3\).

Step1: Multiply \(8x\) and \(x^2\)

Using the rule of exponents \(a^m\times a^n=a^{m + n}\), for \(8x\cdot x^2\), the coefficient is 8, and for the variable part \(x\times x^2=x^{1+2}=x^3\). So the product is \(8x^3\).

Step1: Recall FOIL (Outer: first term of first binomial and second term of second binomial)

The outer terms are \(8x\) (from \(8x-3\)) and \(1\) (from \(x^2 + 1\)). So the expression is \(8x\times1\) (and the product is \(8x\) as given).

Answer:

For the first dropdowns: multiply (for coefficients), add (for exponents). And \((3x)(2x^2)=6x^3\)

Part 2: FOIL for \((8x - 3)(x^2+1)\)

First Term: