Find product: (2 5 a^2b )×(−15b^2ac )× (−1 2 c^2 ) - Vidyadip

Question

Find product:
$\big(\frac{2}{5}\text{a}^2\text{b}\big)×(−15\text{b}^2\text{ac}\big)×\big(\frac{−1}{2}\text{c}^2\big)$

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Answer

To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e. $a ^{ m } \times a ^{ n }= a ^{ m + n }$.
We have:
$\left(\frac{2}{5} a ^2 b \right) \times\left(-15 b ^2 a c \right) \times\left(\frac{-1}{2} c ^2\right)=\left[-\frac{2}{5} \times(-15) \times\left(-\frac{1}{2}\right)\right] \times\left( a ^2 \times a \right)$
$=\big[-\frac{2}{5}×(−15)×(−\frac{1}{2})\big]×\big(\text{a}^{2+1}\big)\\×\big(\text{b}^{1+2}\big)×\big(\text{c}^{1+2}\big)$
$=3\text{a}^3\text{b}^3\text{c}^3$
$\because$ The expression doesn't consist of the variables x and y.
$\therefore$ The result cannot be verified for x = 1 and y = 2
Thus, the answer is $3\text{a}^3\text{b}^3\text{c}^3$

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