Question

completely factor 225c²b + 135c⁸b². how can you check your work?

225c²b + 135c⁸b² =
(simplify your answer. factor completely.)

Explanation:

Step1: Find the GCF of coefficients

Find the GCF of 225 and 135. Prime - factorize: \(225 = 3^{2}\times5^{2}\), \(135 = 3^{3}\times5\). The GCF of 225 and 135 is \(45\).

Step2: Find the GCF of variables

For the variable part, for \(c\) terms, the GCF of \(c^{2}\) and \(c^{8}\) is \(c^{2}\), and for \(b\) terms, the GCF of \(b\) and \(b^{2}\) is \(b\). So the GCF of the two - term expression is \(45c^{2}b\).

Step3: Factor out the GCF

\[

$$\begin{align*} 225c^{2}b + 135c^{8}b^{2}&=45c^{2}b(5 + 3c^{6}b) \end{align*}$$

\]

Step4: Check the work

To check the work, use the distributive property \(a(b + c)=ab+ac\). Here, \(a = 45c^{2}b\), \(b = 5\), and \(c = 3c^{6}b\). Then \(45c^{2}b\times5+45c^{2}b\times3c^{6}b=225c^{2}b + 135c^{8}b^{2}\).

Answer:

\(45c^{2}b(5 + 3c^{6}b)\)