1 / 25

PRESENTATION 12 Basic Algebra

PRESENTATION 12 Basic Algebra. BASIC ALGEBRA DEFINITIONS. A term of an algebraic expression is that part of the expression that is separated from the rest by a plus or minus sign A factor is one of two or more literal and/or numerical values of a term that are multiplied

eisenhart
Download Presentation

PRESENTATION 12 Basic Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PRESENTATION 12 Basic Algebra

  2. BASIC ALGEBRA DEFINITIONS • A term of an algebraic expression is that part of the expression that is separated from the rest by a plus or minus sign • A factor is one of two or more literal and/or numerical values of a term that are multiplied • A numerical coefficient is the number factor of a term • The letter factors of a term are the literal factors

  3. BASIC ALGEBRA DEFINITIONS • Like terms are terms that have identical literal factors • Unlike terms are terms that have different literal factors or exponents

  4. ADDITION • Only like terms can be added. The addition of unlike terms can only be indicated • Procedure for adding like terms: • Add the numerical coefficients, applying the procedure for addition of signed numbers • Leave the variables unchanged

  5. ADDITION • Example: Add 5x and 10x • Add the numerical coefficients 5 + 10 = 15 • Leave the literal factor unchanged 5x + 10x = 15x • Example: –14a2b2 + (–6a2b2) • Add the numerical coefficients and leave the literal factor unchanged –14 + –6 = –20 –14a2b2 + (–6a2b2) = –20a2b2

  6. ADDITION • Procedure for adding expressions that consist of two or more terms: • Group like terms in the same column • Add like terms and indicate the addition of the unlike terms

  7. ADDITION • Example: Add the two expressions 7x + (–xy) + 5xy2 and (–2x) + 3xy + (–6xy2) • Group like terms in the same column • Add the like terms and indicate the addition of the unlike terms

  8. SUBTRACTION • Just as in addition, only like terms can be subtracted • Each term of the subtrahend is subtracted following the procedure for subtraction of signed numbers

  9. SUBTRACTION • Example: Subtract the following expressions (4x2 + 6x – 15xy) – (9x2 – x – 2y + 5y2) • Change the sign of each term in the subtrahend –9x2 + x + 2y – (5y2) • Follow the procedure for addition of signed numbers

  10. MULTIPLICATION • In multiplication, the exponents of the literal factors do not have to be the same to multiply the values • Procedure for multiplying two or more terms: • Multiply the numerical coefficients, following the procedure for multiplication of signed numbers • Add the exponents of the same literal factors • Show the product as a combination of all numerical and literal factors

  11. MULTIPLICATION • Example: Multiply (2xy2)(-3x2y3) • Multiply the numerical coefficients following the procedure for multiplication of signed numbers(2)(-3) = -6 • Add the exponents of the same literal factors(x)(x2) = x1+2 = x3 and (y2)(y3) = y2+3 = y5 • Show the product of coefficients and literal factors(2xy2)(-3x2y3) = -6x3y5

  12. MULTIPLICATION • Procedure for multiplying expressions that consist of more than one term within an expression: • Multiply each term of one expression by each term of the other expression • Combine like terms

  13. MULTIPLICATION • Example: 3a(6 + 2a2) • Multiply each term of one expressions by each term of the other expression = 3a(6) + 3a(2a2) = 18a + 6a3 • Combine like terms; since 18a and 6a3 are unlike terms, they can not be combined = 18a + 6a3

  14. MULTIPLICATION • Example: (3c + 5d2)(4d2 – 2c) • Multiply each term of one expressions by each term of the other expression (FOIL method) 3c (4d2) = 12cd2 (F)irst term 3c(–2c) = –6c2 (O)uter term 5d2(4d2) = 20d4 (I)nner term 5d2(–2c) = –10cd2 (L)ast term • Combine like terms (3c + 5d2)(4d2 – 2c) = 2cd2 –6c2 + 20d4

  15. DIVISION • Procedure for dividing two terms: • Divide the numerical coefficients following the procedure for division of signed numbers • Subtract the exponents of the literal factors of the divisor from the exponents of the same letter factors of the dividend • Combine numerical and literal factors

  16. DIVISION • Example: Divide (-20a3x5y2) ÷ (-2ax2) • Divide the numerical coefficients-20 / -2 = 10 • Subtract the exponentsa3 – 1= a2x5 – 2 = x3y2 = y2 • Combine numerical and literal factors (-20a3x5y2) ÷ (-2ax2) = 10a2x3y2

  17. POWERS • Procedure for raising a single term to a power: • Raise the numerical coefficients to the indicated power following the procedure for powers of signed numbers • Multiply each of the literal factor exponents by the exponent of the power to which it is raised • Combine numerical and literal factors

  18. POWERS • Example: (–4x2y4z)3 • Raise the numerical coefficients to the indicated power (–4)3 = (–4)(–4)(–4) = –64 • Multiply the exponents of the literal factors by the indicated powers (x2y4z)3 = x2(3) + y4(3) + z1(3) = x6y12z3 • Combine (–4x2y4z)3 = –64x6y12z3

  19. POWERS • Procedure for raising two or more terms to a power: • Apply the procedure for multiplying expressions that consist of more than one term

  20. POWERS • Example: (3a + 5b3)2 • Apply the FOIL method 3a(3a) = 9a2 (F)irst term 3a(5b3) = 15ab3 (O)uter term 5b3(3a) = 15ab3 (I)nner term 5b3(5b3) = 25d6 (L)ast term • Combine 9a2 + 30ab3 + 25d6

  21. ROOTS • Procedures for extracting the root of a term: • Determine the root of the numerical coefficient following the procedure for roots of signed numbers • The roots of the literal factors are determined by dividing the exponent of each literal factor by the index of the root • Combine the numerical and literal factors

  22. ROOTS • Example: • Determine the root of the numerical coefficient • Divide the exponent of the literal factors by the index • Combine

  23. REMOVAL OF PARENTHESES • Procedure for removal of parentheses preceded by a plus sign: • Remove the parentheses without changing the signs of any terms within the parentheses • Combine like terms • Example: – 7x + (–4x + 3y – 2) = –7x – 4x + 3y – 2 = –11x + 3y – 2

  24. REMOVAL OF PARENTHESES • Procedure for removal of parentheses preceded by a minus sign: • Remove the parentheses while changing the signs of any terms within the parentheses • Combine like terms • Example: –(7a2 + b – 3) + 12 – (– b + 5) = – 7a2 – b + 3 + 12 + b – 5 = – 7a2 + 10

  25. COMBINED OPERATIONS • Expressions that consist of two or more different operations are solved by applying the proper order of operations • Example: 5b + 4b(5 + a – 2b2) • Multiply 4b(5 + a – 2b2) = 20b + 4ab – 8b3 • Combine like terms 5b + 20b = 25b 25b + 4ab – 8b3

More Related