5.5 Factoring Special Patterns 12/12/12. Perfect Squares 11 1 42 2 93 3 164 4 255 5 366 6 49 7 7 648 8 819 9 100 10 121 11 144 12 169 13.

Slides:

Advertisements

Similar presentations

Advertisements

Squares and Square Roots Objective: Students will be able to successfully multiply and simplify expressions using squares and square roots. Warm-Up Evaluate:

Squares and Square Roots Objective: Students will be able to successfully multiply and simplify expressions using squares and square roots. Warm-Up Evaluate:

Simplifying Radical Expressions Product Property of Radicals For any numbers a and b where and,

People Fractions. Problem 1 of 20 Answer 1 = 10 Problem 2 of 20 Answer 2 = 5.

2.5 Introduction to Complex Numbers 11/7/2012. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of.

2.3 Part 1 Factoring 10/29/2012. What is Factoring? It is finding two or more numbers or algebraic expressions, that when multiplied together produce.

Rational Numbers Jeopardy

5-5 Multiplying Mixed Numbers Learn to multiply mixed numbers.

Factor Special Products April 4, 2014 Pages

Section 8-4 Multiplying and Dividing Rational Expressions.

Factoring Review EQ: How do I factor polynomials?.

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.

3.3 SPECIAL Factoring 12/5/2012. Perfect Squares

By: Ruthie Covington. Directions First you find two fractions. If you have a mixed number, then you multiply the whole number by the denominator.

5.7 Complex Numbers 12/4/2013. Quick Review If a number doesn’t show an exponent, it is understood that the number has an exponent of 1. Ex: 8 = 8 1,

Lesson 0 – 9 Square Roots and Simplifying Radicals

Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

  Different types of Quadratics:  GCF:  Trinomials:  Difference of Squares:  Perfect Square Trinomials: Factoring Quadratics.

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.4 – Complex Numbers.

9.3 Factoring Trinomomials. Rainbow Method (2 nd degree Polynomial) 2.

Warm Up Factor out the GCF 1.-5x x x 3 +4x Factor 3. 4.

5.5 Factoring Special Patterns 11/20/2013. Perfect Squares

Warm Up Day 2 Unit 3A. Use FOIL to Simplify: 1. (x-2)(x+2) 2. (5x + 6)(5x – 6) 3. (x -3)(x+3) 4. (x-1)(x+1)

Radicals Computing with Radicals Target Goals : Add, subtract, multiply, and divide radical expressions.

11.6 Addition and Subtraction: Unlike Denominators.

3.4 Simplify Radical Expressions

7.5 Operations with Radical Expressions. Review of Properties of Radicals Product Property If all parts of the radicand are positive- separate each part.

Unit 5 Solving Quadratics By Square Roots Method and Completing the Square.

6 – 3 Adding, Subtracting and Multiplying Polynomials Day 1 Objective: Add, subtract, and multiply polynomials.

5.3C- Special Patterns for Multiplying Binomials SUM AND DIFFERENCE (a+b)(a-b) = a² - b² (x +2)(x – 2) = x² -4 “O & I” cancel out of FOIL SQUARE OF A BINOMIAL.

Multiplying Binomials

World 1-9 Completing the Square.

Simplifying Radical Expressions

Multiplying Fractions and Mixed Numbers

Radical Functions Unit 3.

8-4 Special Products of Polynomials

Lesson 9.3 Find Special Products of Polynomials

Warm Up Subtract: Add:.

Warm Up Multiply using the F.O.I.L. or Box Method.

Chapter 2 – Polynomial and Rational Functions

Factoring Special Cases :

Completing the Square.

Perfect Square Trinomials

Lesson 7-1 Multiplying Monomials

Simplifying Radical Expressions

Simplifying Radical Expressions.

Warm-Up ***Multiply.

Unit 8 Radicals.

Multiplying Integers SAME SIGNS??? Answer will be POSITIVE. ex)

Solving Harder Rational Equations

Work out (if you can, simplify your answer) 8 6.

Sec 5: Operations with Complex Numbers

Section 7.2 Rational Exponents

5.4 Complex Numbers.

Simplifying Radical Expressions

3.6 Solve Quadratics by Finding Square Roots

7.3 Special Products.

Unit 1.3 Part A Learning Goal:

3.6 Solve Quadratics by Finding Square Roots

Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

Simplifying Radical Expressions

Warm Ups: Give the degree, standard form, and leading coefficient (if possible): 1) 3x3 – 5x4 – 10x + 1 2) 9x – 8 + x2 Factor completely: 3) 4x2.

Chapter 7 – 3 Fractions, Decimals, and Percents

Unit 2 Algebra Investigations

Multiplying Radical Expressions

Presentation transcript:

5.5 Factoring Special Patterns 12/12/12

Perfect Squares

Review Find the product (use FOIL) 1.(x + 2) (x – 2) Answer: x 2 – 4 2. (x + 5) (x – 5) Answer: x 2 – (2x – 3) (2x + 3) Answer: 4x 2 – 9 What’s the pattern???

Difference of Two Squares Pattern (a + b) (a – b) = a 2 – b 2 In reverse, a 2 – b 2 gives you (a + b) (a – b) Examples: 1. x 2 – 4 = x 2 – 2 2 = (x + 2) (x – 2) 2. x 2 – 144 =(x + 12) (x – 12) 3. 4x 2 – 25 = (2x + 5) (2x – 5)

If you can’t remember that, you can still use the big X method. Ex. x 2 – Think of 2 numbers that Multiply to -4 and Add to 0 2 x -2 = = Answer: (x + 2) (x - 2) Ex. x 2 + 0x – 4

Ex. x 2 – Think of 2 numbers that Multiply to -144 and Add to 0 12 x -12 = = Answer: (x + 12) (x - 12) x 2 + 0x – 144

4(-25) = Think of 2 numbers that Multiply to -100 and Add to x 10 = = Answer: (2x - 5) (2x + 5) Factor: 4x Simplify like a fraction. ÷ by Simplify like a fraction. ÷ by 2 4x 2 + 0x - 25

Homework WS