QuestionAugust 24, 2025

Find the product. ((-2)/(9)p+(5)/(3)q)((7)/(9)p-(7)/(2)q)

Find the product. ((-2)/(9)p+(5)/(3)q)((7)/(9)p-(7)/(2)q)
Find the product. ((-2)/(9)p+(5)/(3)q)((7)/(9)p-(7)/(2)q)

Solution
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Answer

\frac{-14}{81}p^2 + \frac{56}{27}pq - \frac{35}{6}q^2 Explanation 1. Apply the distributive property Multiply each term in the first binomial by each term in the second binomial. 2. Calculate individual products (\frac{-2}{9}p) \cdot (\frac{7}{9}p) = \frac{-14}{81}p^2 (\frac{-2}{9}p) \cdot (-\frac{7}{2}q) = \frac{14}{18}pq (\frac{5}{3}q) \cdot (\frac{7}{9}p) = \frac{35}{27}pq (\frac{5}{3}q) \cdot (-\frac{7}{2}q) = -\frac{35}{6}q^2 3. Combine like terms Combine pq terms: \frac{14}{18}pq + \frac{35}{27}pq = \frac{21}{27}pq + \frac{35}{27}pq = \frac{56}{27}pq

Explanation

1. Apply the distributive property<br /> Multiply each term in the first binomial by each term in the second binomial.<br />2. Calculate individual products<br /> $ (\frac{-2}{9}p) \cdot (\frac{7}{9}p) = \frac{-14}{81}p^2 $<br /> $ (\frac{-2}{9}p) \cdot (-\frac{7}{2}q) = \frac{14}{18}pq $<br /> $ (\frac{5}{3}q) \cdot (\frac{7}{9}p) = \frac{35}{27}pq $<br /> $ (\frac{5}{3}q) \cdot (-\frac{7}{2}q) = -\frac{35}{6}q^2 $<br />3. Combine like terms<br /> Combine $pq$ terms: $\frac{14}{18}pq + \frac{35}{27}pq = \frac{21}{27}pq + \frac{35}{27}pq = \frac{56}{27}pq$
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