Factor completely. $$ 48 x^{4} y+36 x^{6} z^{3} $$

Question

UpStudy AI · Accepted Answer

To factor the expression $$ 48 x^{4} y + 36 x^{6} z^{3} $$ completely, follow these steps:

1. **Find the Greatest Common Factor (GCF):**
   - **Numerical coefficients:** The GCF of 48 and 36 is 12.
   - **Variables:** 
     - For $$ x $$, the smallest exponent is $$ x^4 $$.
     - The variables $$ y $$ and $$ z^3 $$ do not have common factors.

2. **Factor out the GCF:**
   $$
   48 x^{4} y + 36 x^{6} z^{3} = 12 x^{4} (4 y) + 12 x^{4} (3 x^{2} z^{3})
   $$
   $$
   = 12 x^{4} (4 y + 3 x^{2} z^{3})
   $$

3. **Check for Further Factoring:**
   The expression inside the parentheses $$ (4 y + 3 x^{2} z^{3}) $$ does not factor further.

**Final Factored Form:**
$$
12 x^{4} (4 y + 3 x^{2} z^{3})
$$

Answer:
$$ 12\, x^{4} \left(4\, y\;+\;3\,x^{2} z^{3}\right) $$
The expression factors to $$ 12x^{4}(4y + 3x^{2}z^{3}) $$.

Factor completely. \[ 48 x^{4} y+36 x^{6} z^{3} \]

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions