Question

multiply (m-n+p) ( m+n-p)​

Answer 1

$\huge {\boxed {\mathbb {QUESTION}}}$

multiply

$(m-n+p) \times ( m+n-p)$

$\huge {\boxed {\mathbb {ANSWER}}}$

$\implies (m-n+p) \times ( m+n-p)$

$\implies m(m+n-p) - n( m+n-p)+p( m+n-p)$

$\implies {m}^{2}+nm-pm- mn-{n}^{2}+pn+mp+np-{p}^{2}$

$\implies {m}^{2}-{n}^{2}-{p}^{2}+\cancel {(nm-nm)} \cancel {(-pm+pm)} (+np+np)$

$\implies{\boxed {\boxed {{m}^{2}-{n}^{2}-{p}^{2}+2np}}}$

$\huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU }}}$

__________________________________________

$\huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$Identities$

${(a\times b)}^{n} ={a}^{n} \times {b}^{n}$

${(\frac{a}{b})}^{n}=\frac{{a}^{n}}{{b}^{n}}$

${a}^{n} \times {a}^{m} ={a}^{n+m}$

$\frac{{a}^{n}} {{a}^{m}} ={a}^{n-m}$

${{a}^{n}}^{m} ={a}^{nm}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$

Answer 2

⟹(m−n+p)×(m+n−p)

\implies m(m+n-p) - n( m+n-p)+p( m+n-p)⟹m(m+n−p)−n(m+n−p)+p(m+n−p)

\implies {m}^{2}+nm-pm- mn-{n}^{2}+pn+mp+np-{p}^{2}⟹m

2

+nm−pm−mn−n

2

+pn+mp+np−p

2

\implies {m}^{2}-{n}^{2}-{p}^{2}+\cancel {(nm-nm)} \cancel {(-pm+pm)} (+np+np)⟹m

2

−n

2

−p

2

+

(nm−nm)

(−pm+pm)

(+np+np)

\implies{\boxed {\boxed {{m}^{2}-{n}^{2}-{p}^{2}+2np}}}⟹

m

2

−n

2

−p

2

+2np