# What is the product of the polynomials below? (6x3 + 3x)(x2 + 4)

May 28, 2018

You have written the question in an odd manner: I will assume you meant
$\left(6 {x}^{3} + 3 x\right) \left({x}^{2} + 4\right)$
In this case:
It is the same as $6 {x}^{3} \left({x}^{2} + 4\right) + 3 x \left({x}^{2} + 4\right)$
so expanding this:
we get
$6 {x}^{5} + 24 {x}^{3} + 3 {x}^{3} + 12 x$ (remember when you times like this ${x}^{3}$ x ${x}^{2}$ you just add the powers)

$6 {x}^{5} + 27 {x}^{3} + 12 x$

May 28, 2018

$6 {x}^{5} + 27 {x}^{3} + 12 x$

#### Explanation:

Use FOIL (First Outer Inside Last)

• First: $6 {x}^{3} \cdot {x}^{2} = 6 {x}^{5}$
• Outer: $6 {x}^{3} \cdot 4 = 24 {x}^{3}$
• Inner: $3 x \cdot {x}^{2} = 3 {x}^{3}$
• Last: $3 x \cdot 4 = 12 x$

Add together and combine like terms.