# Algebra - vocabulary, combing liketerms, multiplyng and factoring polynomials, table

### Vocabulary, combing liketerms, multiplyng and factoring polynomials of algebra

VOCABULARY of algebra |
• • • EX: -4xy has a coefficient of -4; 9m • • EX: 3m • • EX: 4z = 28 is an algebraic equation; 3(a - 4) + 6a = 10 - a is also an algebraic equation; note that both statements have equal signs in them • EX: 50 < -2x is an algebraic inequality; 3(2n + 7) > -10 is an algebraic inequality |

COMBINING LIKE TERMS of algebra |
• You can add or subtract coefficients of like terms to simplify an algebraic expression; when doing so, the value of the exponent does not change EX: 3a + 7a = 10a; 9d EX: Axy |

MULTIPLYING & DIVIDING TERMS |
• Note: Any terms may be multiplied, not just like terms EX: (n • When terms include coefficients, multiply the coefficients and follow the product rule for exponents EX: (4a • EX: (c • When terms include coefficients, raise the coefficients to the power and follow the power rule for exponents EX: (2a • EX: p • When terms include coefficients, divide the coefficients and follow the quotient rule for exponents EX: -27a • EX: x • EX: x |

MULTIPLYING POLYNOMIALS of algebra |
• When a polynomial is multiplied by a monomial, use the distributive property: EX: 4x • When multiplying a polynomial by a polynomial, be sure to multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms; this is often referred to as using the FOIL method for products of binomials; essentially, when multiplying two binomials, multiply each First term, each Outside term, each Inside term, and each Last term; then combine like terms: EX: (2x + y)(3x - 5y) = 2x(3x - 5y) + y(3x - 5y) = 6x |

FACTORING POLYNOMIALS |
• When you factor a polynomial, you are finding what two polynomials multiply together to result in a product of the original polynomial; there are a variety of factoring strategies; when factoring a trinomial (a polynomial with three terms), one common method is to use trial and error by making an educated guess of the first factor in each binomial and an educated guess of the second factor in each binomial, then multiplying the polynomials and adjusting if needed EX: Factor x2 + 7x + 12; try (x + 6)(x + 2); the product is x EX: Factor 6x |

FACTORING SPECIAL POLYNOMIALS |
• To factor a difference of squares, use the rule EX: Factor x x • To factor a difference of cubes, use the rule EX: Factor 8x 8x • To factor a sum of cubes, use the rule EX: Factor 27x 27x |

SOLVING A FIRST-DEGREE EQUATION WITH ONE VARIABLE |
• EX: 1/2·(3a + 5) = 2/3·(7a - 5) + 9 would be multiplied on both sides of the equals sign by the lowest common denominator of 1/2 and 2/3 which is 6; the result would be 3(3a + 5) = 4(7a - 5) + 54; note that only 1/2, 2/3, and 9 were multiplied by 6 and not the contents of the parentheses; the parentheses will be handled in the next step, when the distributive property is used • EX: 3(3a + 5) = 4(7a - 5) + 54 becomes 9a + 15 = 28a - 20 + 54 • EX: 9a + 15 = 28a - 20 + 54 becomes 9a + 15 = 28a + 34 because the only like terms on the same side of the equals sign were -20 and +54 • EX: 9a + 15 = 28a + 34 becomes 9a + 15 - 28a - 15 = 28a + 34 - 28a - 15; note that both -28a and -15 were added to both sides of the equals sign at the same time; this results in -19a = 19 after like terms are added or subtracted • EX: -19a = 19 would be multiplied on both sides by -1/19 (or divided by -19), so the equation would become -19a(-1/19) = 19a(-1/19) or a = -1 • |

SOLVING A FIRST-DEGREE INEQUALITY WITH ONE VARIABLE |
• Follow the same steps for solving a first-degree equality as described above, except for one step in the process; this exception follows: • EX: In 4m > -48, you need to multiply both sides of the > symbol by 1/4; therefore, 4m(1/4) > -48(1/4); this results in m > -12; note that the > did not reverse because you multiplied by a positive 1/4; however, in -5x > 65, you need to multiply both sides by -1/5; therefore, -5x(-1/5) < 65(-1/5); this results in x < -13; note that the > did reverse and become < because you multiplied by a negative number, -1/5 • |

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