By Cynthia Young

The 3rd variation of Cynthia Young’s Algebra & Trigonometry brings jointly all of the parts that experience allowed teachers and beginners to effectively “bridge the gap” among lecture room guideline and autonomous homework by way of overcoming universal studying obstacles and construction self assurance in students’ skill to do arithmetic. Written in a transparent, unmarried voice that speaks to scholars and mirrors how teachers speak in lecture, Young’s hallmark pedagogy permits scholars to develop into self reliant, profitable newcomers. assorted workout varieties and modeling tasks maintain the training clean and motivating. during this variation, younger keeps her culture of fostering a love for succeeding in arithmetic by way of introducing inquiry-based studying tasks, delivering newbies a chance to grasp the fabric with extra freedom whereas reinforcing mathematical talents and instinct.

The seamless integration of Cynthia Young’s Algebra & Trigonometry third variation with WileyPLUS, a research-based, on-line surroundings for potent educating and studying, keeps Young’s imaginative and prescient of creating scholar self belief in arithmetic since it takes the guesswork out of learning by way of offering them with a transparent roadmap: what to do, easy methods to do it, and whether or not they did it correct.

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The most function of those lectures is first to in brief survey the elemental con nection among the illustration thought of the symmetric crew Sn and the idea of symmetric capabilities and moment to teach how combinatorial tools that come up evidently within the thought of symmetric capabilities result in effective algorithms to specific a number of prod ucts of representations of Sn when it comes to sums of irreducible representations.

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A(b ϩ c) ϭ ab ϩ ac 5(x ϩ 2) ϭ 5x ϩ 10 a(b Ϫ c) ϭ ab Ϫ ac 5(x Ϫ 2) ϭ 5x Ϫ 10 Additive identity property Adding zero to any real number yields the same real number. aϩ0ϭa 0ϩaϭa 7y ϩ 0 ϭ 7y Multiplicative identity property Multiplying any real number by 1 yields the same real number. Additive inverse property Multiplicative inverse property a#1ϭa 1#aϭa (8x)(1) ϭ 8x The sum of a real number and its additive inverse (opposite) is zero. a ϩ (Ϫa) ϭ 0 4x ϩ (Ϫ4x) ϭ 0 The product of a nonzero real number and its multiplicative inverse (reciprocal) is 1.

2). 1). EXAMPLE 4 Multiplying a Monomial and a Polynomial Find the product and simplify 5x2(3x5 - x3 + 7x - 4). Solution: ᭤ ᭤ ᭤ 5x2(3x5 - x3 + 7x - 4) ᭤ Use the distributive property. ϭ 5x2(3x5) Ϫ 5x2(x3) ϩ 5x2(7x) Ϫ 5x2(4) Multiply each set of monomials. ■ Answer: 12x4 Ϫ 6x3 ϩ 3x2 ■ YO U R T U R N ϭ 15x7 Ϫ 5x5 ϩ 35x3 Ϫ 20x2 Find the product and simplify 3x2(4x2 Ϫ 2x ϩ 1). How do we multiply two polynomials if neither one is a monomial? For example, how do we ﬁnd the product of a binomial and a trinomial such as (2x Ϫ 5)(x2 Ϫ 2x ϩ 3)?

YO U R T U R N Multiply (2x Ϫ 3)(5x Ϫ 2). qxd 32 8/3/12 11:17 AM Page 32 C H A P T E R 0 Prerequisites and Review Some products of binomials occur frequently in algebra and are given special names. Example 7 illustrates the difference of two squares and perfect squares. EXAMPLE 7 Find the following: Multiplying Binomials Resulting in Special Products a. (x Ϫ 5)(x ϩ 5) b. (x ϩ 5)2 c. (x Ϫ 5)2 Inner r Difference of two squares a. (x - 5)(x + 5) = x + 5x - 5x - 5 = 2 2 r r Outer Last s First r Solution: x2 - 52 = x2 - 25 Inner r r First b.