4.2 Sum And Diff Of Cubes
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Sum and Difference of 2 cubes
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2/27/12 Special Factoring - Sum & Difference of Two Cubes
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Sum and Difference of 2 cubes
The document discusses the formulas for summing and subtracting cubes. It presents the SOAP rule - Sum Of APs, for expanding and factorizing expressions involving sums and differences of cubes. Some examples are given to demonstrate applying the rule, such as expanding y + 8a and factorizing s - st.
Factoring the Difference of Two Squares
The document discusses factoring the difference of two squares. It involves reviewing factoring the difference of two squares, which involves recognizing that the difference of two squares can be written as the product of two binomials, where one binomial contains the sum of the two terms and the other contains their difference.
Factoring the greatest common monomial factor
This document discusses factoring polynomials by finding the greatest common factor (GCF). It explains that factoring a polynomial is the reverse of multiplying a monomial and polynomial. Examples are provided of factoring polynomials by identifying the GCF and rewriting the polynomial as a product of the GCF and other factors. The process of factoring out the GCF is demonstrated step-by-step for several examples.
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The document presents the results of expressing the numbers 1 through 25 as the difference of two squares. It includes a chart showing each number and its solution as two squares subtracted. The group organized the data in a chart and noticed that by adding 0.5 to each number in the solution, they could find the next number in the sequence as the difference of two squares. They hope the audience enjoyed their presentation on differences of squares.
Factoring by Grouping
The document discusses two methods for factoring polynomials: factoring by grouping and factoring by finding a common factor. Factoring by grouping is used when there is no common factor, and it involves grouping terms together that have the same factors. Factoring by finding a common factor involves factoring out the common factor that is present in every term.
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This document provides a summary of factoring strategies and patterns. It outlines a two-step process: 1) factor out the greatest common factor and 2) determine the number of terms and appropriate factoring method, whether it be difference of squares, sum/difference of cubes, trinomials using the AC method, or factoring by grouping for four terms. The goal is for students to learn to recognize and apply the proper factoring strategy based on the polynomial pattern.
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The document is about factoring polynomials, specifically factoring the sum and difference of cubes. It provides the formulas for factoring the sum and difference of cubes, along with examples of factoring expressions using those formulas. It also discusses factoring out the greatest common factor from polynomials.
Simplifying Rational Expressions
The document provides steps for dividing out common factors and factoring rational expressions:
1) Identify common factors in the numerator and denominator and divide them out.
2) Factor the numerator and denominator by identifying common factors in each expression.
3) Divide the factored numerator and denominator, simplifying the expression.
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The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.
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This document contains information and examples about perfect square trinomials in algebra. It defines a perfect square trinomial as having a first term and last term that are perfect squares, with a middle term that is twice the product of the square roots of the first and last terms. Examples are provided to illustrate how to identify if an expression is a perfect square trinomial or not. Several activity cards are included that provide practice identifying, factoring, and giving the factors of perfect square trinomial expressions.
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Special product
The document discusses how algebra builds on previously learned math concepts through newsletters and patterns, highlighting special multiplication patterns like FOIL that allow for mental math computations like squaring and multiplying two-digit numbers, demonstrating how recognizing these patterns helps with factoring polynomials and higher-level algebra skills.
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The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.
Factoring by grouping
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Assessments and examples are available
Can be used by a math teacher in her discussion about factoring
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This document contains information and examples about perfect square trinomials in algebra. It defines a perfect square trinomial as having a first term and last term that are perfect squares, with a middle term that is twice the product of the square roots of the first and last terms. Examples are provided to illustrate how to identify if an expression is a perfect square trinomial or not. Several activity cards are included that provide practice identifying, factoring, and giving the factors of perfect square trinomial expressions.
Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. To simplify rational expressions, we first factor the polynomials and then cancel any common factors. Adding and subtracting rational expressions follows the same process as fractions - find the least common denominator, multiply the numerators and denominators to get the same denominator, then add or subtract the numerators. Multiplying rational expressions involves factoring and cancelling common factors between the numerator and denominator. To divide rational expressions, we multiply the first expression by the reciprocal of the second expression and then factor and cancel. Word problems involving rational expressions can be solved by identifying what is known and unknown, setting up equations relating the known and unknown values, and then solving the equations.
Laws Of Exponents
This document introduces the laws of exponents. It defines key terms like exponent, base, and power. It then outlines six laws of exponents: 1) the product law, 2) the quotient law, 3) the power law, 4) powers with different bases, 5) zero exponents, and 6) negative exponents. It concludes by explaining how to simplify powers and exponential expressions by applying these laws and definitions of exponents.
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Factoring is a financial transaction where a business sells its accounts receivable (invoices) to a third party called a factor at a discount in exchange for immediate money. This allows the business to finance continued operations. Factoring differs from loans in that it involves the purchase of a financial asset rather than assessing creditworthiness, and it involves three parties rather than two. There are various types of factoring including recourse, non-recourse, maturity, and invoice factoring. Factoring provides businesses with financing, accounts receivable maintenance, collection services, and advisory services.
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