Question

Using the pattern from the first figure,

which of the following algebraic expression replaces $b$?

• A. $12x^2{y}^2-24xyz$
• B. $12xyz-24x^2{y}^2$
• C. $12x^2{y}^2-12xyz$
• D. None of the above

Answer 1

The correct option is A $12x^2{y}^2-24xyz$

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.
$3xy-6z+a=7xy-6z\Rightarrow a=4xy$
$\&$
$\left(4xy\right)\times (3xy-6z)=b=12x^2{y}^2-24xyz$