simplify the following (p+q)² - (36q²)/2p² - 50q²

Expand (p+q)²: Question prompt: Simplify the following (p+q)² - (36q²)/2p² - 50q² First, let's expand (p+q)²: (p+q)² = p² + 2pq + q²Rewrite with expanded form: Now, let's rewrite the entire expression with the expanded form: p² + 2pq + q² - (36q²)/2p² - 50q²Simplify (36q²)/2p²: We can simplify (36q²)/2p² by dividing both the numerator and the denominator by 2: (36q²)/2p² = 18q²/p²Rewrite with simplified term: Now, let's rewrite the expression with the simplified term: p² + 2pq + q² - 18q²/p² - 50q²Combine like terms: We can combine like terms q² and -50q²: p² + 2pq + (q² - 50q²) - 18q²/p² p² + 2pq - 49q² - 18q²/p²Leave unlike terms: Now, let's look at the terms -49q² and -18q²/p². Since they are not like terms, we cannot combine them directly. We leave them as they are: p² + 2pq - 49q² - 18q²/p²Final answer: The expression is now simplified as much as possible without further information about p and q. Let's state the final answer: p² + 2pq - 49q² - 18q²/p²

Home

Math Problems

Algebra 2

Simplify rational expressions

Full solution

Q. simplify the following

(p+q)^2 - \frac{36q^2}{2p^2} - 50q^2

Expand $(p+q)^2$ : Question prompt: Simplify the following $(p+q)^2 - \frac{36q^2}{2p^2} - 50q^2$ $\newline$ First, let's expand $(p+q)^2$ : $\newline$ $(p+q)^2 = p^2 + 2pq + q^2$
Rewrite with expanded form: Now, let's rewrite the entire expression with the expanded form: $p^2 + 2pq + q^2 - \frac{36q^2}{2p^2} - 50q^2$
Simplify $(36q^2)/2p^2$ : We can simplify $(36q^2)/2p^2$ by dividing both the numerator and the denominator by $2$ : $(36q^2)/2p^2 = 18q^2/p^2$
Rewrite with simplified term: Now, let's rewrite the expression with the simplified term: $p^2 + 2pq + q^2 - \frac{18q^2}{p^2} - 50q^2$
Combine like terms: We can combine like terms $q^2$ and $-50q^2$ : $\newline$ $p^2 + 2pq + (q^2 - 50q^2) - \frac{18q^2}{p^2}$ $\newline$ $p^2 + 2pq - 49q^2 - \frac{18q^2}{p^2}$
Leave unlike terms: Now, let's look at the terms $-49q^2$ and $-18q^2/p^2$ . Since they are not like terms, we cannot combine them directly. We leave them as they are: $\newline$ $p^2 + 2pq - 49q^2 - 18q^2/p^2$
Final answer: The expression is now simplified as much as possible without further information about $p$ and $q$ . Let's state the final answer: $p^2 + 2pq - 49q^2 - \frac{18q^2}{p^2}$