Find each product. [(2p-3)+q]2

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 51

Chapter 1, Problem 51

Find each product. [(2p-3)+q]²

Verified step by step guidance

Recognize that the expression is a square of a binomial: $[(2p - 3) + q]^2$. This can be treated as $(a + b)^2$ where $a = (2p - 3)$ and $b = q$.

Recall the formula for the square of a binomial: $(a + b)^2 = a^2 + 2ab + b^2$.

Calculate each term separately: first, find $a^2 = (2p - 3)^2$ by expanding it using the formula $(x - y)^2 = x^2 - 2xy + y^2$.

Next, find the middle term $2ab = 2 imes (2p - 3) imes q$ by multiplying the terms carefully.

Finally, find $b^2 = q^2$. Then, combine all three results to write the expanded form of the original expression.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Binomial Expansion

Binomial expansion involves expressing the square of a sum or difference of two terms as a trinomial. For example, (a + b)^2 expands to a^2 + 2ab + b^2. This method helps simplify expressions like [(2p - 3) + q]^2 by applying the formula directly.

Combining Like Terms

After expanding an expression, combining like terms means adding or subtracting terms that have the same variable raised to the same power. This step simplifies the expression into its simplest form, making it easier to interpret or use in further calculations.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It is used to multiply each term inside the parentheses by the term outside or by each other during expansion. This property is fundamental when expanding expressions like [(2p - 3) + q]^2.

Recommended video:

Guided course

04:15

Multiply Polynomials Using the Distributive Property

Related Practice

Textbook Question

Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers. x¹²/x⁸

views

Textbook Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. C ⊆ U

views

Textbook Question

Find each product. [(4y-1)+z]²

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. $2 \frac{5}{8} \div 1 \frac{15}{32}$

Textbook Question

Add or subtract, as indicated. 3/2k + 5/3k

views

Textbook Question

Factor each trinomial, if possible. See Examples 3 and 4. 9m² -12m+4

views