Question $(x+3)^{3}$

Studdy Solution

STEP 1

What is this asking? We need to expand the expression $(x+3)^3$ , which means multiplying $(x+3)$ by itself three times! Watch out! Don't forget to multiply each term in one set of parentheses by each term in the other set of parentheses.
It's easy to miss a term!
Also, don't confuse this with $x^3 + 3^3$ , which is totally different.

STEP 2

1. Expand the first two factors
2. Multiply the result by the third factor
3. Simplify and combine like terms

STEP 3

Let's start by multiplying the first two factors of $(x+3)^3$ , which are $(x+3)$ and $(x+3)$ .

STEP 4

We'll use the FOIL method (First, Outer, Inner, Last) to multiply these binomials: $(x+3) \cdot (x+3) = x \cdot x + x \cdot 3 + 3 \cdot x + 3 \cdot 3$

STEP 5

This simplifies to: $x^2 + 3x + 3x + 9 = x^2 + 6x + 9$ So, the product of the first two factors is $x^2 + 6x + 9$ .

STEP 6

Now, we need to multiply the result from the previous step, $x^2 + 6x + 9$ , by the third factor, $(x+3)$ .

STEP 7

We'll distribute each term of $x^2 + 6x + 9$ to each term of $(x+3)$ : $(x^2 + 6x + 9)(x+3) = x^2(x+3) + 6x(x+3) + 9(x+3)$

STEP 8

Now, let's expand each part of this expression: $x^2(x+3) = x^3 + 3x^2$ $6x(x+3) = 6x^2 + 18x$ $9(x+3) = 9x + 27$

STEP 9

Putting it all together, we get: $x^3 + 3x^2 + 6x^2 + 18x + 9x + 27$

STEP 10

We have some like terms we can combine.
Specifically, we have $3x^2$ and $6x^2$ , and we also have $18x$ and $9x$ .

STEP 11

Combining these like terms gives us: $x^3 + (3x^2 + 6x^2) + (18x + 9x) + 27 = x^3 + 9x^2 + 27x + 27$

STEP 12

Our final answer is $x^3 + 9x^2 + 27x + 27$ !

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms