(6p + 4q)(-2p + 9q)
simplify
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(6p+4q)(-2p+9q).
-12p^2+54pq + -8pq+36q^2
-12p^2 + 36q^2 + 46pq
2(-6p^2+18q^2+23pq)
To simplify the expression (6p + 4q)(-2p + 9q), we can use the distributive property. First, we need to multiply each term from the first set of parentheses by each term from the second set of parentheses.
Let's break it down step by step:
1. Multiply 6p by -2p:
(6p) * (-2p) = -12p^2
2. Multiply 6p by 9q:
(6p) * (9q) = 54pq
3. Multiply 4q by -2p:
(4q) * (-2p) = -8pq
4. Multiply 4q by 9q:
(4q) * (9q) = 36q^2
Now, we combine the like terms:
-12p^2 + 54pq - 8pq + 36q^2
To simplify further, we add or subtract the like terms:
-12p^2 + 54pq - 8pq + 36q^2
Combining like terms:
-12p^2 + 46pq + 36q^2
Therefore, the simplified expression is -12p^2 + 46pq + 36q^2.