From Area Formulas to Algebra

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Presentation transcript:

From Area Formulas to Algebra Panorama 10 From Area Formulas to Algebra

Monomials: A Review A monomial is a term that is made up of a coefficient , variable, and exponent. 3x2

The degree of a monomial is the exponent. If there is more then 1 exponent add them together. Ex: 2x2y2 : degree is 2+2=4 If there is no exponent we assume 1 If there is no coefficient we assume there is a 1

Like Terms Like terms are terms that are the same. For monomials, terms must have the same exponent and the same variable. Which of the following are like terms? 2a, 4a, 3x2, -5x2, 5y , -100ab

Adding and Subtracting monomials Remember your steps Work inside your brackets and drop them. Combine like terms ONLY ADD OR SUBTRACT THE COEFFICIENTS For subtraction change the signs in the brackets after the – sign. Remember if there is no sign we assume positive.

Complete the following 2x + 3x +5x -3y= (2y2-9) + (y2+3)= (3y+2x-8+3x) –(2y –2x+2)= 3a-2a+3y –(2y+3-4a) = (10x2+3x+5) + (2x2+x+7)

Simplifying Algebraic Expressions: Multiplication and Division For simple multiplication use the following steps: Multiply the coefficients Keep the variable Add the exponents Group like terms Ex: 3 x 2y= 6y Ex: 3a2 x 10a = 30a3 Ex: -7y5x 3y2= -21y7

For multiplication of two or more terms by one term use the following steps: Multiply the first term (coefficients only, keep the variables, add exponents) Repeat step 1 for every additional term. Group like terms Ex: 2(3x + 4) Ex: 3x (4x2 – 2x + 10) Ex: 4x3(2x3+12x2-7x+11)

For multiplication of two or more terms by two or more terms use the following steps: Multiply the first term in the first set of brackets by each term in the second set of brackets. Keep the sign that is attached to the term Repeat for every term in the first set of brackets. Group like terms Remember multiply the coefficients, keep the variables, and add the exponents Ex: (4x + 3) (5x – 3) Ex: (3x2- 5) (3x + 2)

Complete the Following (2x – 4) ( 3x + 5) (3x2- 5x + 3) (2x+3) 3x (2x + 3) (5x2 – 3x – 7) (10x2 + 8x + 13) (5x + 2) (4x – 5) (3x + 2x +7 – 5) (6+ 3 – 2x)

For multiplication of terms with two different variables use the following steps: Multiply the coefficients Keep ALL variables Add exponents Group like terms if necessary. Ex: 2a x 3b Ex: (5y + 3x) (5 – 4xy + 3y – 2x)

For division use the following steps: For our classes we will only divide monomials by a constant (just a number) Make sure that your division is in fraction form. Group like terms before you divide. Divide the coefficients by the constant given. Keep the variable and the exponent Ex: 20x2 ÷ 2, 50ab ÷ 5

Homework and Classwork Workbook P 30-34 Textbook P 87-89 # 1-9, 12