Question

From the sum of $5p^2+6pq-7q^2$, $4pq+5q^2$ and $2p^2-3pq$ subtract the sum of $p^2+3pq$ and $4pq+5q^2$.

• A. $6p^2+pq+7q^2$
• B. $6p^2-7q^2$
• C. $6p^2-pq+7q^2$
• D. $6p^2+7q^2$

Answer 1

The correct option is B $6p^2-7q^2$

$\underset{–}{\text{Step 1:}}$
First, let's find the sum of $5p^2+6pq-7q^2$, $4pq+5q^2$ and $2p^2-3pq$. The sum can be evaluated using column method as:



$\underset{–}{\text{Step 2:}}$
Now, we need to find the sum of $p^2+3pq$ and $4pq+5q^2$. This can be evaluated using column method as:


$\underset{–}{\text{Step 3:}}$
Now, we need to subtract the sum obtained in Step 2, $\underset{–}{p^2+7pq+5q^2}$ from the sum obtained in step 1, $\underset{–}{7p^2+7pq-2q^2}$. This can be evaluated using column method as:


Therefore, the required answer is $\underset{–}{6p^2-7q^2}$.

Therefore, option (b.) is the correct choice.