Question

How do you multiply `(4z+3)(z-2)`?

Answer 1

`(4z+3)(z-2) = 4z^2-5z-6`

Explanation:

You have to use the laws of addition and multiplication:
Let me remind you some of these laws.
Commutative law of addition: `A+B=B+A`
Commutative law of multiplication: `A*B=B*A`
Associative law of addition: `(A+B)+C=A+(B+C)`
Associative law of multiplication: `(A * B) * C=A * (B * C)`
Distributive law: `(A+B)*C=A*C+B*C`

Using distributive law, consider
`A=4z`
`B=3`
`C=(z-2)`
Then
`(4z+3)(z-2) = 4z(z-2)+3(z-2)`

Use distributive law again for each term:
`4z(z-2) = 4z^2-8z`
`3(z-2)=3z-6`
Hence,
`(4z+3)(z-2) = 4z^2-8z+3z-6 = 4z^2-5z-6`

NOTE:
We could've started with distributive law by considering
`A=z`
`B=-2`
`C=4z+3`
Then
`(4z+3)(z-2) = (4z+3)z+(4z+3)(-2)`

Another application of distributive law:
`(4z+3)z = 4z^2+3z`
`(4z+3)(-2) = -8z-6`
Hence,
`(4z+3)(z-2) = 4z^2+3z-8z-6 = 4z^2-5z-6`

No surprise, the answer is exactly the same.