Question

Using the pattern from the first figure,
the value of $a+b^2=$

• A. $12y^2{z}^2$
• B. $4y^2{z}^2$
• C. $4yz$

Answer 1

The correct option is A $12y^2{z}^2$

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.
$-4yz+b=-6yz\Rightarrow b=-6yz-(-4yz)\Rightarrow b=-2yz$
$\&$
$(-4yz)\times (-2yz)=a=8y^2{z}^2$

$\Rightarrow a+b^2=12y^2{z}^2$