Find each product. 2b3(b2−$$4b+3)2b^3$(b^2-4b+3)$$

Ch. R - Review of Basic Concepts

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

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 34

Chapter 1, Problem 34

Find each product. $2 b^{3} (b^{2} - 4 b + 3)$

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Identify the expression to be multiplied: $2b^3(b^2 - 4b + 3)$.

Apply the distributive property by multiplying \$2b^3$ with each term inside the parentheses separately.

Multiply \$2b^3$ by the first term: $b^2$. This gives $2b^3 \times b^2 = 2b^{3+2} = 2b^5$.

Multiply \$2b^3$ by the second term: $-4b$. This gives $2b^3 \times (-4b) = -8b^{3+1} = -8b^4$.

Multiply \$2b^3$ by the third term: $3$. This gives $2b^3 \times 3 = 6b^3$. Then, write the product as the sum of these terms: $2b^5 - 8b^4 + 6b^3$.

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Key Concepts

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

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in the other polynomial. This process requires applying the distributive property to combine like terms and simplify the expression.

Exponent Rules

When multiplying terms with the same base, add their exponents. For example, b^3 multiplied by b^2 equals b^(3+2) = b^5. Understanding this rule is essential for correctly simplifying powers during multiplication.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis, which is crucial for expanding expressions like 2b^3(b^2 - 4b + 3).

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Textbook Question

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. $-m $\sqrt{2y^5}$$