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Factor: [tex]64c z^3 + 27c x^3[/tex].

Answer :

To factor the expression [tex]\(64cz^3 + 27cx^3\)[/tex], you can follow these steps:

1. Identify a Common Factor:
Notice that both terms in the expression have a common factor of [tex]\(c\)[/tex]. So, the expression can first be factored as:
[tex]\[
c(64z^3 + 27x^3)
\][/tex]

2. Recognize the Sum of Cubes:
The expression inside the parentheses, [tex]\(64z^3 + 27x^3\)[/tex], is a sum of cubes. This is because:
- [tex]\(64z^3\)[/tex] is [tex]\((4z)^3\)[/tex]
- [tex]\(27x^3\)[/tex] is [tex]\((3x)^3\)[/tex]

3. Use the Sum of Cubes Formula:
The sum of cubes formula is:
[tex]\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\][/tex]
Applying this formula to our expression, the terms are:
- [tex]\(a = 4z\)[/tex]
- [tex]\(b = 3x\)[/tex]

4. Factor Using the Formula:
Substitute [tex]\(a = 4z\)[/tex] and [tex]\(b = 3x\)[/tex] into the formula:
[tex]\[
(4z + 3x)((4z)^2 - (4z)(3x) + (3x)^2)
\][/tex]

5. Calculate Each Part:
- [tex]\(a^2 = (4z)^2 = 16z^2\)[/tex]
- [tex]\(ab = (4z)(3x) = 12zx\)[/tex]
- [tex]\(b^2 = (3x)^2 = 9x^2\)[/tex]

6. Write the Factored Form:
So the expression factors to:
[tex]\[
(4z + 3x)(16z^2 - 12zx + 9x^2)
\][/tex]

7. Include the Common Factor:
Don't forget the common factor we factored out initially:
[tex]\[
c(4z + 3x)(16z^2 - 12zx + 9x^2)
\][/tex]

This gives you the completely factored form of the expression:

[tex]\[ c \cdot (4z + 3x)(16z^2 - 12zx + 9x^2) \][/tex]

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Rewritten by : Barada