Question

please say answer fast​

Answer 1

Question -

m²- 13mn + 40n²

Required Answer -

$\red{\bigstar}\sf m ^{2} - 13mn + 40n ^{2} \large\leadsto{\tt\purple{ [ m - 8n][m-5n ] }}$

Step By Step Solution -

m²- 13mn + 40n² , now we need to replace 13mn from the numbers which are factors of 40 and while adding or subtracting gives 13.

Factors of 40

• 2 and 20
• 4 and 10
• 5 and 8

Let's give a try to each ,

1) 2 and 20 ; 20 + 2 = 22 ☒ , 20 - 2 = 18 ☒

now by adding and subtracting 20and 2 we are not getting - 13

2) 4 and 10 ; 4 + 10 = 14 ☒ , 10 - 4 = 6 ☒

now by adding and subtracting 4 and 10 we are not getting 13

3) 5 and 8 ; 5 + 8 = 13 ☒ , -8 - 5 = -13 ☑

now by adding 8 and 5 we are not getting -13 but by subtracting -8 and 5 we are getting -13 its mean we will replace it with -8 and 5 .

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: {m}^{2} - 8mn - 5mn + {40n}^{2} \\ \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: ({m}^{2} - 8mn )- (5mn + {40n}^{2} )\\ \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: m(m - 8n )- 5n(m - 8n )\\ \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

Now we will take (m-8n) and (m - 4x) common

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \color{lime}{ \: (m - 8n )(m - 5n)}\\ \end{gathered} \end{gathered}\end{gathered} \end{gathered}$