Q. 261 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$10m^4-6250$

Step-by-Step Solution

Answer

The required factors are $10(m^2+25)(m+5)(m-5)$

Step 1. Given Information

The given expression is $10m^4-6250$

Step 2. Calculation

We will find the factors by taking common factor out from the expression and then use the difference of square patterns.
$$\begin{gathered} 10m^4-6250=10(m^4-625) \\ =10({\left(m^2\right)}^2-{\left(25\right)}^2) \\ =10(m^2+25)(m^2-25) \\ =10(m^2+25)(m^2-5^2) \\ =10(m^2+25)(m+5)(m-5) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 10(m^2+25)(m+5)(m-5)=10(m^2+25)(m^2-5^2) \\ =10(m^2+25)(m^2-25) \\ =10({\left(m^2\right)}^2-{\left(25\right)}^2) \\ =10(m^4-625) \\ =10m^4-6250 \end{gathered}$$