Example 1

Simplify the expressions.

a) [[$ 4 \cdot 3x = 12x $]]​
b) [[$ 2 \cdot (-4y) = 2 \cdot (-4) \cdot y = -8y $]]​
c) ​[[$ -5x^2 \cdot (-3) = -5 \cdot (-3) \cdot x^2 = 15x^2 $]]​
d) [[$ 3 \cdot (-xy) = 3 \cdot (-1) \cdot xy = -3xy $]]​

Example 2

Calculate the products of the following monomials.

a) [[$ 2x \cdot (-3x) = 2 \cdot (-3) \cdot x \cdot x = -6x^2 $]]​
b) [[$ 4a \cdot 5b = 4 \cdot 5 \cdot a \cdot b = 20ab $]]​
c) [[$ -x \cdot (-3y) = (-1) \cdot (-3) \cdot x \cdot y = 3xy $]]​
d) [[$ 2y \cdot 4y^2 \cdot (-y^2) = 2 \cdot 4 \cdot (-1) \cdot y \cdot y^2 \cdot y^2 =-8 \cdot y^{(1+2+2)} = -8y^5 $]]​
e) [[$ -5ab \cdot 2a = -5 \cdot 2 \cdot a \cdot a \cdot b = -10a^2b $]]​