Question
Factorise : $2(ab+cd) - a^2- b^2+ c^2+ d^2$
✓
Answer
$2(ab+cd) - a^2- b^2+ c^2+ d^2$
$= 2ab + 2cd - a^2 - b^2 + c^2 + d^2$
$= c^2+ d^2 + 2cd - a^2 - b^2 + 2ab$
$= ( c^2 + d^2 + 2cd ) - ( a^2 + b^2 - 2ab )$
$= ( c + d )^2 - ( a - b )^2$
$= ( c + d + a - b )( c + d - a + b )$
$= 2ab + 2cd - a^2 - b^2 + c^2 + d^2$
$= c^2+ d^2 + 2cd - a^2 - b^2 + 2ab$
$= ( c^2 + d^2 + 2cd ) - ( a^2 + b^2 - 2ab )$
$= ( c + d )^2 - ( a - b )^2$
$= ( c + d + a - b )( c + d - a + b )$
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