Question

using identity evaluate 203×204, 103×97,(997)², 53²-47²​

Answer 1

Answer:

$203×204=(200+3)(200+4)=200^{2}+(3+4)200+3×4=40000+7×200+12=40000+1400+12=41412$

$103×97=(100+3)(100-3)=100^{2}-3^{2} = 10000-9=9991$

$997^{2}=(1000-3)^{2}=1000^{2}-2×1000×3+3^{2}=1000000-6000+9=994009$

$53^{2}-47^{2} = (53+47)(53-47) = 100×6=600$