Question

Find each of the following product:
(−4x²) × (−6xy²) × (−3yz²)

Answer 1

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:

\[\left( - 4 x^2 \right) \times \left( - 6x y^2 \right) \times \left( - 3y z^2 \right)\]

\[ = \left\{ \left( - 4 \right) \times \left( - 6 \right) \times \left( - 3 \right) \right\} \times \left( x^2 \times x \right) \times \left( y^2 \times y \right) \times z^2 \]

\[ = \left\{ \left( - 4 \right) \times \left( - 6 \right) \times \left( - 3 \right) \right\} \times \left( x^{2 + 1} \right) \times \left( y^{2 + 1} \right) \times z^2 \]

\[ = - 72 x^3 y^3 z^2\]

Thus, the answer is \[- 72 x^3 y^3 z^2\].