Question

factorise x^2+x-(a+1)(a+2)​

Answer 1

To factorise :

x² + x - ( a + 1 )( a + 2 )

Solution -

x² + x - ( a + 1 )( a + 2 )

=> x² + [ ( a + 2 ) - ( a + 1 ) ] x - ( a + 1 )( a + 2 )

=> x² + (a + 2) x - (a - 1 )x - ( a + 1 )( a + 2 )

=> x [ x + a + 2 ] - ( a + 1 ) [ x + a + 2 ]

=> [ x + a + 2 ][ x - a - 1 ] .

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 + 2ca

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Answer 2

Question :-

${x}^{2} + x - (a + 1)(a + 2)$

Solution :-

${x}^{2} + x - (a + 1)(a + 2)$

${x}^{2} + {(a + 2)(a + 1)} \times x - (a + 1)(a + 2)$

${x}^{2} + (a + 2)x - (a - 1)x - (a + 1)(a + 2)$

$x(x + a + 2) - (a - 1)(x + a + 2)$

$(x + a + 2)(x - a - 2)$

Extra information :-

$(a + b )^{2} = {a}^{2} + {b}^{2} + 2.a.b$

$(a - b) ^{2} = {a}^{2} + {b}^{2} - 2.a.b$

${a}^{2} - {b}^{2} = (a + b)(a - b)$