Question

Factor completely the binomial. 121x^4y^6 - 25x^2z^12. Show ALL your work and EXPLAIN ALL your steps using COMPLETE sentences. question is above thanks

Answer 1

The expression is given below as

`121x^4y^6-25x^2z^(12)`

Step 1:

Factor out the common term

The common term is

`=x^2`
`\begin{gathered} 121x^4y^6-25x^2z^(12) \\ x^2((121x^4y^6)/(x^2)-(25x^2z^(12))/(x^2)) \\ x^2(121x^2y^6-25z^(12)) \\ \text{note:} \\ (x^4)/(x^2)=x^(4-2)=x^2 \\ (x^2)/(x^2)=x^(2-2)=x^0=1 \end{gathered}`

Step 2:

Expand the bracket using a figure of two squares

`\begin{gathered} x^2(121x^2y^6-25z^(12)) \\ 121x^2y^6=(11xy^3)^2,25z^(12)=(5z^6)^2 \\ By\text{ substituting the expressions, we will have} \\ x^2(121x^2y^6-25z^(12))=x^2((11xy^3)^2-(5z^6)^2) \end{gathered}`

Step 3:

Apply the difference of two squares principle below

`a^2-b^2=(a-b)(a+b)`
`x^2((11xy^3)^2-(5z^6)^2)=x^2(11xy^3-5z^6)(11xy^3+5z^6)`

Hence,

The final answer is

`x^2(11xy^3-5z^6)(11xy^3+5z^6)`