Multiply (6z2 - 4z + 1)(8 - 3z).
Answers
Answer
Explanation
(6z² - 4z + 1) (8 - 3z)
=> 8 (6z² - 4z + 1) - 3z ( 6z² - 4z + 1)
=> 48z² - 32z + 8 - 18z³ + 12z² - 3z
=> 18z³ + 60z³ -35z + 8
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Answer:
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When multiplying polynomials, as we see here, we must distribute everything.
Every term that is in the trinomial
6
z
2
−
4
z
+
1
must be multiplied individually by both terms in the following binomial
8
−
3
z
. Then, all these multiplied terms will be added to one another to form a large polynomial.
Let's break down what we'll multiply:
(
6
z
2
−
4
z
+
1
)(
8
−
3
z
1
(
8
−
3
−
4
z
(
8
−
3
6
z
2
(
8
−
3
z
)
)
So, we see that the
(
8
−
3
z
)
term is distributed to each term within
(
6
z
2
−
4
z
+
1
)
.
Adding these all together, we see that
(
6
z
2
−
4
z
+
1
)
(
8
−
3
z
)
=
6
z
2
(
8
−
3
z
)
+
(
−
4
z
)
(
8
−
3
z
)
+
1
(
8
−
3
z
)
Distributing each, we obtain
=
48
z
2
−
18
z
3
+
−
32
z
+
12
z
2
+
8
−
3
z
Now, to simplify, sort this by degree (combine like terms):
=
−
18
z
3
+
48
z
2
+
12
z
2
48
+
12
=
60
−
32
z
−
3
z
−
32
−
3
=
−
35
+
8
=
−
18
z
3
+
60
z
2
−
35
z