Regents Review #1 Expressions

Simplifying Expressions What does it mean to simplify an expression? CARRY OUT ALL OPERATIONS! PEMDAS is always in effect!

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

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

Simplifying Exponential Expressions When simplifying exponential expressions, remember… Use exponent rules to simplify When dividing, all results appear in the numerator. Change negative exponents to positive by moving them to the other part of the fraction No decimals or fractions are allowed in any part of the fraction

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

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

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

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

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

Polynomials When dividing polynomials, each term in the numerator is divided by the monomial that appears in the denominator. 4)

What does it mean to factor? Create a “multiplication problem”. Factoring What does it mean to factor? Create a “multiplication problem”.

Factoring There are three ways to factor Factor out the GCF AM factoring 3) DOTS

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

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

Rational Expressions 2) 3) When multiplying, factor and cancel out common factors in the numerators and denominators of the product. 2) When dividing, multiply by the reciprocal, then factor and divide out common factors in the numerators and denominators of the product. 3)

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 FORM OF ONE Ex:

Rational Expressions 4) Multiply by FOO Multiply by FOO simplified

Radicals When simplifying radicals, create a product using the largest perfect square (4,9,16,25,36,49.64,81,100). 1) When multiplying radicals, multiply coefficients and multiply radicands. 2)

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

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)

Writing Algebraic Expressions 1) Express the cost of y shirts bought at x dollars each. xy Express “three times the quantity of 4 less than a number” as an expression. 3(x – 4)

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

Now it’s your turn to review on your own Now it’s your turn to review on your own! Using the information presented today and your review packet, complete the practice problems in the packet. Regents Review #2 is FRIDAY, May 10th BE THERE!!!!