Question

Factorise: x^2 - 18x - 19 + 20y -y^2

Answer 1

$x^{2}-18x-19+20y-y^{2} \\= \\x^{2} - 18x - 19 - ( y^{2} - 20y )= x^{2} - 2 \times x \times 9 + 9^{2} - 9^{2} -19 -[ y^{2} - 2\times y \times 10 + 10^{2} - 10^{2} ] \\= ( x - 9 )^{2} - 81 - 19 - ( y - 10 )^{2} +100 \\= </p><p>( x - 9 )^{2} - 100 - ( y - 10 )^{2} +100 \\= ( x - 9 )^{2} - - ( y - 10 )^{2} \\= [ (x-9)+(y-10)][ (x-9) - (y-10)] \\= (x-9+y-10)(x-9-y+10) \\= (x+y-19)(x-y+1)$

Therefore.,

$\red{Factors \:of \:x^{2}-18x-19+20y-y^{2}}$

$\green {= (x+y-19)(x-y+1)}$

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