Question
Find following product:
$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times\left(-3 y z^2\right)$
$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times\left(-3 y z^2\right)$
✓
Answer
To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, $a^{ m } \times a ^{ n }= a ^{ m + n }$.
We have:
$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times\left(-3 y z^2\right)$
$=[(-4) \times(-6) \times(-3)] \times\left(x^2 \times x\right) \times\left(y^2 \times y\right) \times z^2$
${[(-4) \times(-6) \times(-3)] \times\left(x^2+1\right) \times\left(y^2+1\right) \times z^2}$
$=-72 x^3 y^3 z^2$
We have:
$\left(-4 x^2\right) \times\left(-6 x y^2\right) \times\left(-3 y z^2\right)$
$=[(-4) \times(-6) \times(-3)] \times\left(x^2 \times x\right) \times\left(y^2 \times y\right) \times z^2$
${[(-4) \times(-6) \times(-3)] \times\left(x^2+1\right) \times\left(y^2+1\right) \times z^2}$
$=-72 x^3 y^3 z^2$
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