Question

Multiply the pair conjugates by using Product of Conjugates Pattern. ( simplify) (m + 8n/9) (m - 8n/9)

Answer 1

the Answer:

The expression is given below as

`(m+(8)/(9)n)(m-(8)/(9)n)`

Concept:

The multiplication of conjugates by using product of conjugates pattern is given below as

`\begin{gathered} (a-b)(a+b) \\ =a(a+b)-b(a+b) \\ =a^2+ab-ab-b^2 \\ (a-b)(a+b)=a^2-b^2 \end{gathered}`

By comparing coefficient, we will have

`a=m,b=(8)/(9)n`
`\begin{gathered} (m+(8)/(9)n)(m-(8)/(9)n)=m^2-((8)/(9)n)^2 \\ (m+(8)/(9)n)(m-(8)/(9)n)=m^2-(64)/(81)n^2 \end{gathered}`

Hence,

The final answer is given below as

`m^2-(64)/(81)n^2`