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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 19
Capitolo 1, Problema 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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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.
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Finding Zeros & Their Multiplicity

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.
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Multiply Polynomials Using the Distributive Property

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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Combinations
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