Math / Algebra

QuestionKuta Software - Infinito 1 Factoring Monomi Write the prime factor 1) $25 n^{2}$ 3) $12 a$

Studdy Solution

STEP 1

What is this asking? We need to break down these expressions into their smallest prime number building blocks! Watch out! Don't forget to factor the numbers completely and include all the variables!

STEP 2

1. Factor $25n^2$
2. Factor $12a$

STEP 3

Alright, let's factor $25n^2$ !
First, we look at the number $25$ .
What are the prime factors of $25$ ?
Well, $25$ is $5$ times $5$ , and $5$ is a prime number!
So, we can write $25$ as $5 \cdot 5$ or $5^2$ .

STEP 4

Now, let's look at the variable part, $n^2$ .
This means $n$ multiplied by itself, or $n \cdot n$ .

STEP 5

Putting it all together, we get $25n^2 = 5 \cdot 5 \cdot n \cdot n = 5^2 \cdot n^2$ .
Boom!

STEP 6

Now, let's tackle $12a$ !
We start by factoring the number $12$ . $12$ is $2 \cdot 6$ .
But wait! $6$ isn't prime. $6$ is $2 \cdot 3$ .
So, $12$ is $2 \cdot 2 \cdot 3$ or $2^2 \cdot 3$ .

STEP 7

Next, we have the variable $a$ .
Since it's just $a$ , we keep it as is.

STEP 8

Combining everything, we get $12a = 2 \cdot 2 \cdot 3 \cdot a = 2^2 \cdot 3 \cdot a$ .
Awesome!

STEP 9

$25n^2 = 5^2 \cdot n^2$ $12a = 2^2 \cdot 3 \cdot a$

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QuestionKuta Software - Infinito 1 Factoring Monomi Write the prime factor 1) $25 n^{2}$ 3) $12 a$

Studdy Solution

STEP 1

What is this asking? We need to break down these expressions into their smallest prime number building blocks! Watch out! Don't forget to factor the numbers completely and include all the variables!

STEP 2

1. Factor $25n^2$
2. Factor $12a$

STEP 3

Alright, let's factor $25n^2$ !
First, we look at the number $25$ .
What are the prime factors of $25$ ?
Well, $25$ is $5$ times $5$ , and $5$ is a prime number!
So, we can write $25$ as $5 \cdot 5$ or $5^2$ .

STEP 4

Now, let's look at the variable part, $n^2$ .
This means $n$ multiplied by itself, or $n \cdot n$ .

STEP 5

Putting it all together, we get $25n^2 = 5 \cdot 5 \cdot n \cdot n = 5^2 \cdot n^2$ .
Boom!

STEP 6

Now, let's tackle $12a$ !
We start by factoring the number $12$ . $12$ is $2 \cdot 6$ .
But wait! $6$ isn't prime. $6$ is $2 \cdot 3$ .
So, $12$ is $2 \cdot 2 \cdot 3$ or $2^2 \cdot 3$ .

STEP 7

Next, we have the variable $a$ .
Since it's just $a$ , we keep it as is.

STEP 8

Combining everything, we get $12a = 2 \cdot 2 \cdot 3 \cdot a = 2^2 \cdot 3 \cdot a$ .
Awesome!

STEP 9

$25n^2 = 5^2 \cdot n^2$ $12a = 2^2 \cdot 3 \cdot a$

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QuestionKuta Software - Infinito 1 Factoring Monomi Write the prime factor 1) 25n225 n^{2}25n2 3) 12a12 a12a

Studdy Solution

STEP 1

What is this asking? We need to break down these expressions into their smallest prime number building blocks! Watch out! Don't forget to factor the numbers completely and include *all* the variables!

STEP 2

1. Factor 25n225n^225n22. Factor 12a12a12a

STEP 3

Alright, let's **factor** 25n225n^225n2!First, we look at the number 252525.What are the prime factors of 252525?Well, 252525 is 555 times 555, and 555 is a prime number!So, we can write 252525 as 5⋅55 \cdot 55⋅5 or 525^252.

STEP 4

Now, let's look at the variable part, n2n^2n2.This means nnn multiplied by itself, or n⋅nn \cdot nn⋅n.

STEP 5

Putting it all together, we get 25n2=5⋅5⋅n⋅n=52⋅n225n^2 = 5 \cdot 5 \cdot n \cdot n = 5^2 \cdot n^225n2=5⋅5⋅n⋅n=52⋅n2.Boom!

STEP 6

Now, let's tackle 12a12a12a!We start by **factoring** the number 121212. 121212 is 2⋅62 \cdot 62⋅6.But wait! 666 isn't prime. 666 is 2⋅32 \cdot 32⋅3.So, 121212 is 2⋅2⋅32 \cdot 2 \cdot 32⋅2⋅3 or 22⋅32^2 \cdot 322⋅3.

STEP 7

Next, we have the variable aaa.Since it's just aaa, we keep it as is.

STEP 8

Combining everything, we get 12a=2⋅2⋅3⋅a=22⋅3⋅a12a = 2 \cdot 2 \cdot 3 \cdot a = 2^2 \cdot 3 \cdot a12a=2⋅2⋅3⋅a=22⋅3⋅a.Awesome!

STEP 9

25n2=52⋅n225n^2 = 5^2 \cdot n^225n2=52⋅n2 12a=22⋅3⋅a12a = 2^2 \cdot 3 \cdot a12a=22⋅3⋅a

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QuestionKuta Software - Infinito 1 Factoring Monomi Write the prime factor 1) $25 n^{2}$ 3) $12 a$

What is this asking? We need to break down these expressions into their smallest prime number building blocks! Watch out! Don't forget to factor the numbers completely and include all the variables!

1. Factor $25n^2$
2. Factor $12a$

Alright, let's factor $25n^2$ !
First, we look at the number $25$ .
What are the prime factors of $25$ ?
Well, $25$ is $5$ times $5$ , and $5$ is a prime number!
So, we can write $25$ as $5 \cdot 5$ or $5^2$ .

Now, let's look at the variable part, $n^2$ .
This means $n$ multiplied by itself, or $n \cdot n$ .

Putting it all together, we get $25n^2 = 5 \cdot 5 \cdot n \cdot n = 5^2 \cdot n^2$ .
Boom!

Now, let's tackle $12a$ !
We start by factoring the number $12$ . $12$ is $2 \cdot 6$ .
But wait! $6$ isn't prime. $6$ is $2 \cdot 3$ .
So, $12$ is $2 \cdot 2 \cdot 3$ or $2^2 \cdot 3$ .

Next, we have the variable $a$ .
Since it's just $a$ , we keep it as is.

Combining everything, we get $12a = 2 \cdot 2 \cdot 3 \cdot a = 2^2 \cdot 3 \cdot a$ .
Awesome!

$25n^2 = 5^2 \cdot n^2$ $12a = 2^2 \cdot 3 \cdot a$