# How do you multiply (3x^2 + 2x + 4)(2x + 1)?

Apr 24, 2018

$6 {x}^{3} + 7 {x}^{2} + 10 x + 4$

#### Explanation:

You have to take each number in the first bracket and multiply it by the second one.
First lets do $3 {x}^{2}$
$\left(3 {x}^{2}\right) \cdot \left(2 x\right)$ and (3x^2)*1 This will give 6x^3$\mathmr{and}$3x^2#

Then $2 x$
$2 x \cdot 2 x$ and $2 x \cdot 1$
This will give $4 {x}^{2}$ and $2 x$

Then $4$
$4 \cdot 2 x$ and $4 \cdot 1$
This will give $8 x$ and $4$

Taking all these, you simply just add them together!

Apr 24, 2018

$= 6 {x}^{3} + 7 {x}^{2} + 10 x + 4$

#### Explanation:

Do the first term in the first bracket multiplied by the first term in the second bracket. Do the same with the first term in the first bracket ($3 {x}^{2}$) and the second term of the second bracket.

($3 {x}^{2}$)x($2 x$) = $6 {x}^{3}$
($3 {x}^{2}$)x($1$) = $3 {x}^{2}$

[For powers, use the rule:

${a}^{m}$x${a}^{n}$ = ${a}^{m} + n$ (where $x$ is actually ${x}^{1}$ from example above which simply calculates to $x$)

Then multiply any real numbers as you normally would ($3$x$2$)]

For the next step, multiply the second term of the first bracket to the first of the second bracket:

($2 x$)x($2 x$) = $4 {x}^{2}$
($2 x$)x($1$) = $2 x$

Proceed to the final term in the first bracket and follow the same steps:

($4$)x($2 x$) = $8 x$
($4$)x($1$) = $4$

Simplify by adding all like terms together:

$= 6 {x}^{3} + 3 {x}^{2} + 4 {x}^{2} + 2 x + 8 x + 4$
$= 6 {x}^{3} + 7 {x}^{2} + 10 x + 4$