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

$(m+\frac{8}{9}n)(m-\frac{8}{9}n)$

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=\frac{8}{9}n$$\begin{gathered} (m+\frac{8}{9}n)(m-\frac{8}{9}n)=m^2-(\frac{8}{9}n)^2 \\ (m+\frac{8}{9}n)(m-\frac{8}{9}n)=m^2-\frac{64}{81}n^2 \end{gathered}$

Hence,

The final answer is given below as

$m^2-\frac{64}{81}n^2$