Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 19

Chapter 1, Problem 19

Find each product. (x+7)(x+3)

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Identify the problem as multiplying two binomials: $(x+7)(x+3)$.

Apply the distributive property (also known as FOIL method) to multiply each term in the first binomial by each term in the second binomial: First, Outer, Inner, Last.

Multiply the First terms: $x \times x = x^2$.

Multiply the Outer terms: $x \times 3 = 3x$ and the Inner terms: $7 \times x = 7x$.

Multiply the Last terms: $7 \times 3 = 21$, then combine all terms: $x^2 + 3x + 7x + 21$, and finally combine like terms $3x + 7x$.

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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 multiplying each term in one polynomial by each term in the other. For binomials like (x+7)(x+3), this means applying the distributive property to combine all products of terms.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is used to multiply each term inside one binomial by each term in the other, ensuring all parts are accounted for in the product.

Combining Like Terms

After multiplying, terms with the same variable and exponent are combined to simplify the expression. For example, terms with x are added together to write the product in standard polynomial form.

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