Question

Fill in the blanks:​

(vii) $1\times 8=\underset{–}{}$ $\text{and}$ $a^{2}x{y}^2\times 8a^3{x}^{2}y=\underset{–}{}$

Answer 1

Find the product of $1$ and $8$
To find: $1\times 8$
$\therefore 1\times 8=8$

Find the product of $a^{2}x{y}^2$ and $8a^3{x}^{2}y$
To find: $a^{2}x{y}^2\times 8a^3{x}^{2}y$

The multiplication of monomials can be performed by multiplication of their coeffficients and literals.

$\therefore a^{2}x{y}^2\times 8a^3{x}^{2}y$
$=(1\times 8)\times (a^{2}x{y}^2\times a^3{x}^{2}y)$
$=8\times a^{2+3}\times x^{1+2}\times y^{2+1}$
$=8a^5{x}^3{y}^3$
Hence, $1\times 8=8$ and $a^{2}x{y}^2\times 8a^3{x}^{2}y=8a^5{x}^3{y}^3$
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