Questions: Factor (20 a+16 a^3).

Transcript text: Factor $20 a+16 a^{3}$.

Solution

Solution Steps

To factor the expression $20a + 16a^3$, we need to find the greatest common factor (GCF) of the terms and factor it out. The GCF of $20a$ and $16a^3$ is $4a$. We then divide each term by $4a$ and write the expression as a product of the GCF and the resulting polynomial.

Step 1: Identify the Expression

We start with the expression $20a + 16a^3$.

Step 2: Find the Greatest Common Factor

The greatest common factor (GCF) of the coefficients $20$ and $16$ is $4$. Additionally, both terms contain the variable $a$, with the lowest power being $a^1$. Therefore, the GCF is $4a$.

Step 3: Factor the Expression

We factor out the GCF $4a$ from the expression: \[ 20a + 16a^3 = 4a(5 + 4a^2) \]