(6p + 4q)(-2p + 9q)
simplify
please help
( 6 p + 4 q ) ( - 2 p + 9 q ) =
6 p * ( - 2 p ) + 4 q * ( - 2 p ) + 6 p * 9 q + 4 q * 9 q =
- 12 p ^ 2 - 8 p q + 54 p q + 36 q ^ 2 =
- 12 p ^ 2 + 46 p q + 36 q ^ 2
To simplify the expression (6p + 4q)(-2p + 9q), you can use the distributive property. The distributive property states that multiplying a sum by a number is the same as multiplying each term in the sum by that number and then adding them up.
Here's how to simplify the expression step by step:
1. Multiply the first terms of each binomial:
(6p) * (-2p) = -12p^2
2. Multiply the first term of the first binomial by the second term of the second binomial:
(6p) * (9q) = 54pq
3. Multiply the second term of the first binomial by the first term of the second binomial:
(4q) * (-2p) = -8pq
4. Multiply the second terms of each binomial:
(4q) * (9q) = 36q^2
5. Now, combine all the simplified terms:
-12p^2 + 54pq - 8pq + 36q^2
6. Finally, simplify further if possible:
Combine like terms -54pq and -8pq to get -62pq.
The simplified expression is: -12p^2 - 62pq + 36q^2.
Therefore, the simplified form of (6p + 4q)(-2p + 9q) is -12p^2 - 62pq + 36q^2.