Question

Using the identity $(x+a)(x+b)=x^2+(a+b)x+ab$, find the values of the following:
$55\times 56$

Answer 1

Value of $55\times 56,$ using identity $(x+a)(x+b)=x^2+(a+b)x+ab$

$\Rightarrow 55\times 56=(50+5)\times (50+6)={\left(50\right)}^2+(5+6)\left(50\right)+(5\times 6)$

$=2500+(11\times 50)+30$

$=2500+550+30$

$=3080$

Hence, the answer is $3080.$