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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 61
Chapter 6, Problem 61

Find each product, if possible.
[312532][3−6430]\(\left\)[ \(\begin{matrix}\) \(\sqrt{3}\) & 1 \\ 2\(\sqrt{5}\) & 3\(\sqrt{2}\) \(\end{matrix}\) \(\right\)] \(\left\)[ \(\begin{matrix}\) \(\sqrt{3}\) & -\(\sqrt{6}\) \\ 4\(\sqrt{3}\) & 0 \(\end{matrix}\) \(\right\)]

Verified step by step guidance
1
Identify the expressions or polynomials that need to be multiplied. This could be binomials, trinomials, or other polynomial forms.
Apply the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial. For example, if multiplying \((a + b)(c + d)\), multiply \(a\) by \(c\) and \(d\), then multiply \(b\) by \(c\) and \(d\).
Write down all the products obtained from the distribution step, ensuring no terms are missed.
Combine like terms by adding or subtracting coefficients of terms that have the same variable parts and exponents.
Simplify the expression fully to write the final product in standard polynomial form, arranging terms in descending order of degree.

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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 two or more polynomials by applying the distributive property. Each term in the first polynomial is multiplied by every term in the second polynomial, and like terms are combined to simplify the result.
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Finding Zeros & Their Multiplicity

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential in algebra for expanding expressions and multiplying polynomials by distributing each term across the sum inside parentheses.
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Multiply Polynomials Using the Distributive Property

Combining Like Terms

After multiplying polynomials, like terms—terms with the same variable raised to the same power—must be combined by adding or subtracting their coefficients. This simplifies the expression into its standard polynomial form.
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Combinations
Related Practice
Textbook Question

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x2 + y2 = 25 at only one point.

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

Textbook Question

Graph the solution set of each system of inequalities.

y≤x3−xy\(\le\) x^3-x

y>−3y>-3

Textbook Question

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

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Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

∣3−65−102−13−6420−7311∣\(\begin{vmatrix}\)3&-6&5&-1\\0&2 &-1&3\\-6&4&2&0\\-7&3&1&1\(\end{vmatrix}\)

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