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Simplifying Exponential Expressions and Polynomials Guide

Understand how to simplify exponential expressions and polynomials, including scientific notation, factoring, rational expressions, and radicals. Practice problems included.

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Simplifying Exponential Expressions and Polynomials Guide

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  1. Regents Review #1 Expressions Roslyn Middle School Research Honors Integrated Algebra

  2. Simplifying Expressions What does it mean to simplify an expression? CARRY OUT ALL OPERATIONS!

  3. Simplifying Exponential Expressions 1) xy0 2) (2x2y)(4xy3) 3) (2x3y5)4 x(1) 8x3y4 24(x3)4(y5)4 x 16x12y20 any nonzero number multiply coefficients raise each factor to raised to the zero power add exponents to the power equals one

  4. Simplifying Exponential Expressions 6) 4) 5) divide coefficients subtract exponents move negative exponents and rewrite as positive simplify numerator and denominator coefficients by dividing by a common factor raise numerator and denominator to the power of the fraction

  5. Simplifying Exponential Expressions When simplifying exponential expressions, remember… • Use exponent rules to simplify • When dividing, all results appear in the numerator. If negative exponents appear in the numerator, move them to the denominator and rewrite them with positive exponents. • Never ever allow a decimal to appear in the numerator or denominator of your expression! All expressions should have integer coefficients in the numerator and denominator!!!

  6. Scientific Notation Writing numbers in scientific notation • 345,000,000 = 3.45 108 2) 0.0000109 = 1.09 10-5

  7. Scientific Notation Multiplying and Dividing Numbers in Scientific Notation 3) 4)

  8. Polynomials When adding polynomials, combine like terms! • (3x – 2) + (5x – y) + (2x – 4) 3x +5x +2x– 2– 4– y 10x – 6 – y

  9. Polynomials When subtracting polynomials, distribute the minus sign before combining like terms! • Subtract 5x2 – 2y from 12x2 – 5 12x2 – 5y – (5x2 – 2y) 12x2 – 5y – 5x2 + 2y 12x2 – 5x2– 5y + 2y 7x2 – 3y

  10. Polynomials When multiplying polynomials, distribute each term from one set of parentheses to every term in the other set of parentheses. 3) 4)

  11. Polynomials When dividing polynomials, each term in the numerator is divided by the monomial that appears in the denominator. 5)

  12. Factoring What does it mean to factor? Factoring is the opposite of simplifying. To factor means to create a product from a simplified expression. It is important to know how to factor because it helps you simplify expressions!

  13. Factoring There are three ways to factor • Pull out the GCF • AM factoring 3) DOTS

  14. Factoring When factoring completely, factor until you cannot factor anymore! 1) 2) 3)

  15. Rational Expressions When simplifying rational expressions (algebraic fractions), factor and cancel out factors that are common to both the numerator and denominator. 1) 2)

  16. Rational Expressions When multiplying, factor and cancel out common factors in the numerators and denominators of the product. 3) When dividing, multiply by the reciprocal, then factor and cancel out common factors in the numerators and denominators of the product. 4)

  17. Rational Expressions • When adding and subtracting rational expressions, find a common denominator. • Create equivalent fractions using the common denominator(Multiply by FOOs) • Add or subtract numerators and keep the denominator the same. • Simplify your final answer if possible.

  18. Rational Expressions 5) Multiply by FOO Multiply by FOO simplified

  19. Rational Expressions 6) FOO

  20. Radicals When simplifying radicals, create a product using the largest perfect square. 1) When multiplying radicals, multiply coefficients and multiply radicands. 2)

  21. Radicals When dividing radicals, divide coefficients and divide radicands. 3) A fraction is not simplified, if a radical appears in the denominator! 4)

  22. Radicals When adding or subtracting radicals, simplify all radicals. If radicals have “like” radicands, then add or subtract coefficients and keep the radicands the same. 5) In order to get like radicals, simplify each radical.

  23. Writing Algebraic Expressions 1) Express the cost of yshirts bought at x dollars each. xy 2) Express the number of inches in f feet. 12f

  24. Evaluating Algebraic Expressions Evaluate x2 – y when x = -2 and y = -5 x2 – y (-2)2 – (-5) 4 + 5 9

  25. Regents Review #1Now it’s time to study!Using the information from this power point and your review packet, complete the practice problems.

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