Question

Solve the above question with suitable identity.
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Answer 1

Question :-

Solve the above question with suitable identity.

$\sf (m^2 - n^2 m)^2 + 2 m^3n^2$

Answer :-

Identity used -

• $\sf (a - b)^2 = a^2 + b^2 - 2ab$

Solution -

➩ $\sf (m^2 - n^2 m)^2 + 2 m^3n^2$

Using the identity -

• $\sf (a - b)^2 = a^2 + b^2 - 2ab$

➩ $\sf (m^2)^2 + (n^2m)^2 - 2(m^2)(n^2m) + 2m^3n^2$

➩ $\sf m^4 + n^2m^2 - \cancel{2 m^3n^2} + \cancel{2 m^3n^2}$

➩ $\sf m^4 + n^2m^2$

$\boxed{\sf (m^2 - n^2 m)^2 + 2 m^3n^2 = m^4 + n^2m^2}$

Answer 2

Question

${ \boxed{ \bf{ \rm{(m^{2} - n {}^{2} m ){}^{2} + 2m {}^{3} n {}^{2} }}}}$

Solve with suitable identity

Answer

${ \bf{ \rm{(m^{2} - n {}^{2} m ){}^{2} + 2m {}^{3} n {}^{2} }}}$ is in the form of$\tt \: (a - b) {}^{2} \: where \tt \: a = m {}^{2} \: and \: b \: = n {}^{2} m$

We know,

${ \boxed{ \tt \: (a - b) {}^{2} = a {}^{2} - 2ab + b {}^{2} }}$

Substituting the values.

$\boxed { \tt \: (m {}^{2} - n {}^{2} m) {}^{2}} = \tt m {}^{2}² - 2(m²)(n {}^{2}m) + (n {}^{2} m) {}^{2}$

$\tt\mapsto m {}^{4} - \cancel{2m {}^{3}n {}^{2} }+ n {}^{2} m {}^{2} + \cancel{2m {}^{3} n {}^{2} }$

$\tt\mapsto m {}^{4} + n {}^{2} m {}^{2}$

${ \boxed { \boxed{\tt\mapsto m {}^{4} + n {}^{2} m {}^{2} }} }$

Basic formulas↓

${ \color{lightgreen}{\boxed {\boxed {\begin{array}{c} \tt \: (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab\\ \: \tt(a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab\\ \: \tt \:(a - b)(a + b) = a {}^{2} - b {}^{2} \: \end{array}}}}}$