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ALEGBRA

ALEGBRA. MONOMIALS ALGEBRAIC EXPRESSIONS ADDING/ SUBRTACTING MULTIPLYING/ DIVIDING DISTRIBUTION EQUATIONS. MONOMIALS. A monomial with variable x is the product of a real number by a non-negative integer exponent co-efficient variable

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ALEGBRA

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  1. ALEGBRA MONOMIALS ALGEBRAIC EXPRESSIONS ADDING/ SUBRTACTING MULTIPLYING/ DIVIDING DISTRIBUTION EQUATIONS

  2. MONOMIALS • A monomial with variable x is the product of a real number by a non-negative integer exponent co-efficientvariable • -3x² is a monomial where -3 is the coefficient, x is the variable, and 2 is the exponent. • The degree of a monomial in one variable corresponds to the exponent of the variable. • The degree of a monomial with many variables is equal to the sum of the exponents.

  3. MONOMIALS • Degree of the monomial = the sum of all the exponents making up the monomial EX. 6x²y³ - 2 variables and a Degree of 5 (2 + 3) • The numerical value of a monomial is calculated by replacing (substituting) the variable by a value (Follow BEDMAS) EX. x = 3, y = 2: 6 x 3² x 2³ = 6 x 9 x 8 = 432 • Assumptions: - no sign = positive - no sign = multiply - no number = 1

  4. monomials • ADDING & SUBTRACTING “LIKE” TERMS (SIMILAR MONOMIALS) EX. 4x + 6x = 10x or 4x – 6x = -2x EX. 4x² + 6x + 3 + 2x + 5 + 4x² = 8x² + 8x + 8 or 4x² - 6x - 3 - 2x + 5 + 4x² = 8x² - 8x + 2 • MULTIPLYING & DIVIDING MONOMIALS EX. (VARIABLE x CONSTANT) MULTIPLY / DIVIDE CO-EFFICIENT 4 x 5a = 20a or 8a ÷ 2 = 4a EX. (MONOMIAL x MONOMIAL) MULTIPLY / DIVIDE CO-EFFIECIENT AND ADD / SUBTRACT VARIABLES 3a x 2a = 6a² or 3a x -2b = -6ab 8a³÷ 4a² = 2a or 12a ÷ 6b = 2ab

  5. ALGEBRAIC EXPRESSIONS • Made up of a monomial or the sum of monomials • + 3x • Simplify monomials to create an algebraic expressionby adding and subtracting like terms • 4 - 8x + 5 - 2 + 7x + 3 - 2 - = 2 - 3 - x + 8

  6. ADDING / SUBTRACTING • To determine the sum or difference of algebraic expressions, apply the distributive property of multiplication over addition. EX. Two negatives = positive • (2x + 5) + (3x – 4) = 2x + 3x + 5 – 4 = 5x + 1 * signs stays the same with addition • (2x + 5) – (3x – 4) = 2x - 3x + 5 + 4 = -x + 9 * signs are opposite for brackets with subtraction sign in front

  7. MULTIPLY / DIVISION • To multiply or divide an algebraic expression by a constant, we apply the distributive property of multiplication or division over addition. Basically multiply/dividing each monomial in the brackets seperately by the constant • 3 x (2a + 5b) = (3 x 2a) + (3 x + 5b) = 6a + 15b • (12m + 20n) ÷ 4 = (12m ÷ 4) + (20n ÷ 4) = 3m + 5n

  8. DISTRIBUTION • To multiply or divide an algebraic expression with another algebraic expression, we apply the distributive property of multiplication or division over addition for both expressions. The term is called F.O.I.L. (Firsts, Outsides, Insides, Lasts) • (4x + 2) • (3x + 5) • Firsts 4x • 3x = 12 • Outsides 4x • 5 = 20x • Insides 2 • 3x = 6x • Lasts 2 + 5 = 7 • Add/Subtract “like” terms 20x + 6x = 26x • Answer 12 + 26x + 7

  9. EQUATIONS • 3 styles of equation questions • 1) SIMPLIFY – 4x² - 6x - 3 - 2x + 5 + 4x² = 8x²- 8x + 2 • 2) FIND FOR THE VARIABLE – 4x + 12 = 4 (what is the value of x?) 4x = 4 – 12 or 4x = -8 x = -2 • 3) SUBSTITUTION – 2x²- 5x + 2 (if x = 2) 2(2)²- 5(2) + 2 8 – 10 + 2 = 0

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