Question

Observe the pattern of the first figure to find the values of $a$ & $b$ in the second figure.If $x=1,$ then the value of $b-a=$

Answer 1

From the first figure pattern, we can observe that
$\text{term in east direction i.e.}xy$
$+$
$\text{term in west direction i.e.}{x}^2$
$=\text{term in south direction i.e.}{x}^2+xy$
$\&$
$\text{term in east direction i.e.}xy$
$\times$
$\text{term in west direction i.e.}{x}^2$
$=\text{term in north direction i.e.}{x}^{3}y$

According to the same pattern, we can find $a\&b$ values in the second pattern.
$7x\times a=7x^{2}y\Rightarrow a=\frac{7x^{2}y}{7x}=\Rightarrow a=xy$
$\&$
$7x+a=b\Rightarrow 7x+xy=b$
$b-a=7x+xy-xy=7x$
$\therefore \text{At}x=1,$
$\text{the value of}(b-a)=7\times 1$
$=7$