What is the product of 2p + q and –3q – 6p + 1?
–12p2 – 6pq – 4p – 3q + 1
–12p2– 12pq + 2p – 3q2 + q
–9p2q2 + 12pq – 2p + q
12p2 + 12pq +2p + 3q2 + q
–12p2– 12pq + 2p – 3q2 + q
To find the product of 2p + q and –3q – 6p + 1, we will use the distributive property. First, multiply 2p + q by -3q:
(2p + q) * -3q
= -6p*q - 3q^2
Next, multiply 2p + q by -6p:
(2p + q) * -6p
= -12p^2 - 6pq
Finally, multiply 2p + q by 1:
(2p + q) * 1
= 2p + q
Now, add all the terms together to get the final expression:
-12p^2 - 6pq - 6pq - 3q^2 + 2p + q
Combining like terms, the product simplifies to:
-12p^2 - 12pq - 3q^2 + 2p + q +1
Therefore, the product of 2p + q and –3q – 6p + 1 is -12p^2 - 12pq - 3q^2 + 2p + q +1.
To find the product of 2p + q and –3q – 6p + 1, you can use the distributive property. This means you need to multiply each term of the first expression by each term of the second expression and then combine like terms.
Let's go step by step:
1. First, multiply 2p by each term of the second expression:
- 2p * -3q = 6pq
- 2p * -6p = -12p^2
- 2p * 1 = 2p
2. Next, multiply q by each term of the second expression:
- q * -3q = -3q^2
- q * -6p = -6pq
- q * 1 = q
3. Now, combine all the terms:
-6pq - 12p^2 + 2p - 3q^2 + q
So, the product of 2p + q and –3q – 6p + 1 is:
-6pq - 12p^2 + 2p - 3q^2 + q
Therefore, the correct option is: -6pq - 12p^2 + 2p - 3q^2 + q.