We appreciate your visit to Simplify the expression tex 6x 3 48 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure, let's break this down step-by-step:
We start with the expression:
[tex]\[ 6x^3 + 48 \][/tex]
1. Identify the Greatest Common Factor (GCF):
We need to factor out the common term from the expression. To do this, we first find the greatest common factor (GCF) of the coefficients and the constant term. In this case, both terms 6 and 48 have a common factor, which is 6.
2. Factor out the GCF:
Once we have identified the GCF, we factor it out from each term in the expression:
[tex]\[
6x^3 + 48 = 6(x^3) + 6(8)
\][/tex]
Now, factor out the 6:
[tex]\[
6(x^3 + 8)
\][/tex]
3. Consider special factoring forms:
Notice that [tex]\(x^3 + 8\)[/tex] is a sum of cubes. The sum of cubes formula is given by:
[tex]\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\][/tex]
Here, [tex]\(x^3\)[/tex] is [tex]\(a^3\)[/tex] and [tex]\(8\)[/tex] is [tex]\(2^3\)[/tex]. Therefore, [tex]\(a = x\)[/tex] and [tex]\(b = 2\)[/tex].
4. Apply the sum of cubes formula:
Substitute [tex]\(a = x\)[/tex] and [tex]\(b = 2\)[/tex] into the sum of cubes formula:
[tex]\[
(x)^3 + (2)^3 = (x + 2)((x)^2 - (x)(2) + (2)^2)
\][/tex]
Simplify inside the parentheses:
[tex]\[
(x + 2)(x^2 - 2x + 4)
\][/tex]
5. Combine everything back together:
Now, bring back the factored out GCF:
[tex]\[
6(x + 2)(x^2 - 2x + 4)
\][/tex]
So, the factorization of the original expression:
[tex]\[ 6x^3 + 48 \][/tex]
is:
[tex]\[ 6(x + 2)(x^2 - 2x + 4) \][/tex]
This is the simplified, factored form of the given expression.
We start with the expression:
[tex]\[ 6x^3 + 48 \][/tex]
1. Identify the Greatest Common Factor (GCF):
We need to factor out the common term from the expression. To do this, we first find the greatest common factor (GCF) of the coefficients and the constant term. In this case, both terms 6 and 48 have a common factor, which is 6.
2. Factor out the GCF:
Once we have identified the GCF, we factor it out from each term in the expression:
[tex]\[
6x^3 + 48 = 6(x^3) + 6(8)
\][/tex]
Now, factor out the 6:
[tex]\[
6(x^3 + 8)
\][/tex]
3. Consider special factoring forms:
Notice that [tex]\(x^3 + 8\)[/tex] is a sum of cubes. The sum of cubes formula is given by:
[tex]\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\][/tex]
Here, [tex]\(x^3\)[/tex] is [tex]\(a^3\)[/tex] and [tex]\(8\)[/tex] is [tex]\(2^3\)[/tex]. Therefore, [tex]\(a = x\)[/tex] and [tex]\(b = 2\)[/tex].
4. Apply the sum of cubes formula:
Substitute [tex]\(a = x\)[/tex] and [tex]\(b = 2\)[/tex] into the sum of cubes formula:
[tex]\[
(x)^3 + (2)^3 = (x + 2)((x)^2 - (x)(2) + (2)^2)
\][/tex]
Simplify inside the parentheses:
[tex]\[
(x + 2)(x^2 - 2x + 4)
\][/tex]
5. Combine everything back together:
Now, bring back the factored out GCF:
[tex]\[
6(x + 2)(x^2 - 2x + 4)
\][/tex]
So, the factorization of the original expression:
[tex]\[ 6x^3 + 48 \][/tex]
is:
[tex]\[ 6(x + 2)(x^2 - 2x + 4) \][/tex]
This is the simplified, factored form of the given expression.
Thanks for taking the time to read Simplify the expression tex 6x 3 48 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
