Question

X2 - x - ( a - 3 ) ( a - 2 )

Answer 1

Factorise : x² - x - ( a - 3)( a - 2 ) .

Solution :

x² - x - (a - 3)( a - 2)

=> x² - [ ( a - 2 ) - ( a - 3 ) ] x - ( a - 3)( a - 2 ) .

=> x² - ( a - 2 )x + ( a - 3 ) x - ( a - 3)( a - 2 )

=> x [ x - a + 2 ] + ( a - 3 ) [ x - a + 2 ]

=> [ x - a + 2 ][ x + a - 3 ] .

This is the required answer .

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Additional Information -

( a - b )² = a² - 2ab + b²

( a + b )² = a² + 2ab + b²

( a - b )( a + b ) = a² - b²

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac

( a + b - c )² = a² + b² + c² + 2ab - 2bc - 2ac

( a - b + c )² = a² + b² + c² - 2ab - 2bc + 2ac

( -a + b + c )² = a² + b² + c² - 2ab + 2bc - 2ac

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Answer 2

Question

${x}^{2} - x - (a - 3)(a - 2)$

Solution

${x}^{2} - x - (a - 3)(a - 2)$

$= > {x}^{2} ((a - 2) - (a - 3))x - (a - 3)(a - 2)$

$= > {x}^{2} - (a - 2)x + (a - 3)x - (a - 3)(a - 2)$

$= > {x}^{2} (x - a + 2) + (a - 3)(x - a + 2)$

$= > (x - a + 2)(x + a - 3)$

Hence, the answer of the equation is (x-a+2)(x+a-3)

$\huge \red{ \boxed{ \underline{extra \: explanation}}}$

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$(x + y + z) ^{3} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx$

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$(x + y) ^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$

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$(x - y) ^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$

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${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

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$(x - y) ^{2} = {x}^{2} +{y}^{2} - 2xy$

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${x}^{2} - {y}^{2} = (x + y)(x - y)$