Question - Expanding and Simplifying Algebraic Expressions
mathcombining like termssimplifying algebraic expressionsexpanding algebraic expressionsdistributing terms
Solution:
3p(p - q) - (2p - q)²Step 1: Distribute 3p in the first term= 3p² - 3pqStep 2: Expand the square in the second term= (2p - q)(2p - q)= 4p² - 2pq - 2pq + q²Step 3: Combine like terms in the second term= 4p² - 4pq + q²Step 4: Subtract the expanded second term from the first term= (3p² - 3pq) - (4p² - 4pq + q²)Step 5: Distribute the subtraction across each term in the parentheses= 3p² - 3pq - 4p² + 4pq - q²Step 6: Combine like terms= -p² + pq - q²The final answer:= -p² + pq - q²
Tutor Solution:
To solve the expression given in the image, we need to apply the distributive property and simplify the expression step by step. The given expression is:\[ 3p(p - q) - (2p - q)^2 \]Step 1: Apply the distributive property to the first termThe distributive property states that for all real numbers a, b, and c, the expression a(b + c) equals ab + ac. Let's apply it to the first term:\[ 3p(p - q) = 3p \cdot p - 3p \cdot q = 3p^2 - 3pq \]Step 2: Expand the squared termThe second term $$(2p - q)^2$$ is a binomial squared, which can be expanded using the formula $$(a - b)^2 = a^2 - 2ab + b^2$$. Let's apply it:\[ (2p - q)^2 = (2p)^2 - 2 \cdot 2p \cdot q + q^2 = 4p^2 - 4pq + q^2 \]Step 3: Combine the expanded termsNow we combine the expanded terms:\[ 3p^2 - 3pq - (4p^2 - 4pq + q^2) \]Step 4: Simplify the expressionNext, distribute the negative sign through the second term:\[ 3p^2 - 3pq - 4p^2 + 4pq - q^2 \]Step 5: Combine like termsCombine terms that have the same variables raised to the same powers:\[ (3p^2 - 4p^2) + (-3pq + 4pq) - q^2 \]\[ -p^2 + pq - q^2 \]So the simplified expression is:\[ -p^2 + pq - q^2 \]Remember to keep track of the signs while combining like terms, and be careful to apply the distributive property correctly in the early steps. The final expression represents the simplified version of the original expression.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com