Expand each of the following a 2 52 5b 3 43 4 c 5 25

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2.Expand each of the following:a)(2? − 5)(2? + 5)b)(3? + 4)(3? − 4)c)(5? − 2)(5? + 2)d)(−2? + 3)(−2? − 3)e)(7 − 2?)(7 + 2?)f)(2ℎ − 𝑘)(2ℎ + 𝑘)g)(6? + 5)(6? − 5)h)(5? − ?)(5? + ?)i)(2? − 11)(2? + 11)j)(?2− ?)(?2+ ?)3.Use the algebraic identities to evaluate each of the following:a)502 × 498b)305 × 295c)98 × 102d)12032e)9012f)8992g)8922h)8052i)692+ 138 + 1j)782+ 312 + 44.If ?2+ ?2= 14and ?? = 5, find the value of (? + ?)5.Given that ? + ? = 10and ?2− ?2= 40, find the value of ? − ?6.If ?2+ ?2= 86and ?? = −16, find the value of (? − ?)7.If (? + ?)2= 361and ?? = −120, calculate the value of ?2+ ?8.Using algebraic rules and without using a calculator, evaluatea)2342382362362b)167161164164182c)8888889088888888888888898888888829.The figure shows ABCD as a trapezium in which ?? = (5? + 6)cm, ?? = 3?cm and the height between the parallel lines is (4? − 3)cm. Show that the area of the trapezium can be expressed as (16?2− 9)cm22..2.2..
MATH 120 College Algebra Chapter 1: Expansion and Factorization of Algebraic ExpressionsPage 5 Factorization of Algebraic Expressions Objectives In this section, students will learn how to factorize simple algebraic expressions by using the reverse of the distributive law as well as by grouping; factorize quadratic expressions; solve quadratic equations by factorization. Example-10:Factorize each of the following. a)2 + 6?b)5? + 15?c)3?2+ 9?d)2𝜋?2+ 2𝜋?ℎe)2?? + 4?? − 8???f)?2?3− ?5?2+ 2?4?6Example-11:Factorize each of the following. a)?? + 4? + 3? + 12b)?2+ ?? − 3? − 3?c)?2− ?? − 2? + 2?d)?3− ?2− 1 + ?e)(? + 2?)2− (? + 2?)(3? − 7?)Exercise 1D 1.Factorize each of the following.a)8? + 2b)4? − 20c)2?2+ 6?d)5?? − 25??e)3?3− 12?2?f)10?2− 18?g)4?? − 12???h)14?? − 49?2i)3?2? + 6??2+ 3???2j)10?3+ 15?? + 20??2.Factorize each of the following.a)? + ?? + 2? + 2?2b)?2+ 3?? + 2? + 6?c)2?? + 2?? + ?? + ??d)3?? + 3?? + 2?? + 2??e)?? + ?? + ?? + ?2f)?2− 3? + 2?? − 6?g)6?? − 4? − 2? + 3??h)2?? + ?? − 2?? − 4??i)?? − 3? − 3? + ??j)3?? − ?? + 6?? − 2??
MATH 120 College Algebra Chapter 1: Expansion and Factorization of Algebraic ExpressionsPage 6 3.Factorize each of the following where possible.a)pqqpp321b)2222rprpqrqpc)aaxxx77492d)qrprpqp84632e)aaaa3264234f)3222255xyxyyxyxg))302(52baah))(242baxxi))12(23mmmj))2(2)4(nmpnmpFactorization Using Algebraic Identities Keywords: perfect squares, the difference of two squares Example-12:Factorize the following. a)?2+ 6? + 9b)?2− 12? + 36c)𝑘2− 81d)9?2− 4Example-13:Evaluate the following by factorization a)79 × 83 − 69 × 83b) 1032− 9Exercise 1E1.Factorize each of the following.a)?2+ 8? + 16b)?2+ 4? + 4c)?2+ 6? + 9d)2?2+ 4? + 2e)3?2+ 12? + 12f)4?2+ 32? + 64g)?2− 6? + 9h)?2− 8? + 16i)2− 4ℎ + 4j)2?2− 4? + 22.Factorize each of the following.a)?2+ 2?? + ?2b)?2+ 6?? + 9?2c)16?2+ 8?? + ?2d)9?2+ 24?? + 16?2e)4?2+ 8?? + 4?2f)25?2− 10?? + ?2g)49?2− 42?? + 9?23.Factorize each of the following where possible.a)?2− 4b)?2− 16c)𝑘2− 81d)25?2− 64e)36?2− 49f)81 − 16?2
MATH 120 College Algebra Chapter 1: Expansion and Factorization of Algebraic ExpressionsPage 7 g)64 − 9?2h)−4ℎ2+ 81i)2?2− 18j)3?2− 1474.Factorize each of the following completely.a)22khb)2216yxc)22254dcd)2236bae)22949dcf)22502yxg)22273yxh)22464bai)2241hk5.

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