Question

factorise
I) m² - (b-c)²​

Answer 1

m² - (b-c)²

m² - b² - c² + 2bc

Answer 2

Answer:

$\boxed{ \bf\:{m}^{2} - {(b - c)}^{2} = (m + b - c) \: (m - b + c) \: }$

Step-by-step explanation:

Given expression is

$\sf \: {m}^{2} - {(b - c)}^{2}$

We know,

$\boxed{ \sf\: {x}^{2} - {y}^{2} = (x + y)(x - y) \: }$

So, using this algebraic identity, we get

$\sf \: = \: [m + (b - c)] \: [m - (b - c)]$

$\sf \: = \: (m + b - c) \: (m - b + c)$

Hence,

$\implies\boxed{ \bf\:{m}^{2} - {(b - c)}^{2} = (m + b - c) \: (m - b + c) \: }$

$\rule{190pt}{2pt}$

Additional Information:

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$