Multiplying Binomials using the Grid Method Feb. 2007 S. Calahan.

Slides:

Advertisements

Similar presentations

10.5: Factoring Trinomials (Reverse FOIL) Integrated Math 2.

Advertisements

Factoring Quadratic Expressions ax 2 + bx + c. 2x2x 3x3x +3 – 4 Setting the Stage Do you remember how to multiply these together? (Referred to as FOIL.

Divide Polynomial by Monomial 3x 2 + 6x 3x = 3x 2 3x + 6x 3x = 3xx 3x + 32x32x = x x 2 y - 6xy + 12y 6xy = 6  3xxy 6xy  2y 6xy = 3x 1 x.

Long Multiplication What is long multiplication?

EXAMPLE 1 Solve a quadratic equation by finding square roots Solve x 2 – 8x + 16 = 25. x 2 – 8x + 16 = 25 Write original equation. (x – 4) 2 = 25 Write.

Multiplying Polynomials

Solving 2-step equations ax + b = c. Keep it balanced Just like when solving a one- step equation keep it balanced. Just like when solving a one- step.

x + 5 = 20 x+5 20 (-5) x + 5 = 20 x 20 (-5) x + 5 = 20.

Quadratic Expressions and Equations Expanding quadratic expressions using the grid method (C)

Do Now: Evaluate Multiplying Monomials Objectives SWBAT: 1) multiply monomials 2) Simplify expressions involving powers of monomials.

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.

12.6A Adding Rational Expressions with SAME denominators.

Factoring Polynomials

Factoring, Difference of Two Squares

Инвестиционный паспорт Муниципального образования «Целинский район»

Factoring by GCF. Factoring Put the expression in a division tower Continue to divide by numbers or variables until there is no number or variable common.

How to Multiply using Lattice. Step 1: How many boxes to you need? 23 X 5 You need 2 boxes on top and 1 on the side.

Ch 8.5 (part 2) Factoring ax 2 + bx + c using the Grouping method Objective: To factor polynomials when a ≠ 1.

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

13.01 Polynomials and Their Degree. A polynomial is the sum or difference of monomials. x + 3 Examples: Remember, a monomial is a number, a variable,

(x – 8) (x + 8) = 0 x – 8 = 0 x + 8 = x = 8 x = (x + 5) (x + 2) = 0 x + 5 = 0 x + 2 = x = - 5 x = - 2.

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Multiplying Polynomials Module VII, Lesson 3 Online Algebra

Warm Up Week 1 1) 2( x + 4 ) 2x 2 = 50 2x + 8 x = ±5 2)

MULTIPLYING POLYNOMIALS. OBJECTIVE NCSCOS 1.01 b – Write equivalent forms of algebraic expressions to solve problems. Operate with polynomials Students.

Divide a polynomial by a binomial

Multiplying a polynomial by a monomial 8-6 objective: Students will find the product of a polynomial and a monomial. To solve equations involving polynomials.

Multiplying by 2-digit factors Partial Products. How can we multiply 23 × 15 1.Draw a box and divide it into four pieces. 2.Write the value of each digit.

Aim: How do we divide polynomials? Divide each term of the polynomial by the monomial. Factor each expression. Divide out the common factors in each.

Step 1: Place x 2 term and constant into the box 2x 2 2 PROBLEM: 2x 2 + 5x + 2.

Multiply: a) x(x + 7) b) 6x(x 2  4x + 5) Solution a) x(x + 7) = x  x + x  7 = x 2 + 7x b) 6x(x 2  4x + 5) = (6x)(x 2 )  (6x)(4x) + (6x)(5) = 6x 3.

Dividing Polynomials The objective is to be able to divide a polynomial by a monomial.

What is a Conjugate? Conjugates are pairs of binomials involving radicals that, when multiplied together, become rational (the radicals disappear). Pairs.

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Multiply the coefficients, the 2 and the -3 to get -6 a 3 * a 2 will be a 5, you add exponents when you multiply terms b 1 * b 4 will be b 5.

EXAMPLE 3 Multiply polynomials vertically

Chapter 6.4.  Reminder: What are we trying to do when we solve an inequality?  Answer:  To get the variable by itself.

X2x2 + x x 2 +3x +2 +2x x + 2 x 2 + x +2x +2 Learning how to do long multiplication with number and algebra.

Multiplying Polynomials

Multiplying Polynomials with FOIL Objective: Students will multiply two binomials using the FOIL method. S. Calahan March 2008.

Multiplying Binomials. -Distributive Property 2x(x + 3) = 2x(x) + 2x(3) = 2x 2 + 6x Prior Knowledge.

F-O-I-L A method for Multiplying 2 Binomials. F-O-I-L FOIL stands for: First Outer Inner Last Find the product of each set of terms and add them up to.

Warm – Up #1 What do you find in common with the following algebraic expression? 2

9-2 Factoring Using the Distributive Property Objectives: 1)Students will be able to factor polynomials using the distributive property 2)Solve quadratic.

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n) Algebra S9 Day 21.

Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +

Solving Equations. An equation links an algebraic expression and a number, or two algebraic expressions with an equals sign. For example: x + 7 = 13 is.

Long multiplication – column method

照片档案整理一、照片档案的含义二、照片档案的归档范围三、卷内照片的分类、组卷、排序与编号四、填写照片档案说明五、照片档案编目及封面、备考填写六、数码照片整理方法七、照片档案的保管与保护.

공무원연금관리공단 광주지부 공무원대부등 공적연금 연계제도 공무원연금관리공단 광주지부. 공적연금 연계제도 국민연금과 직역연금 ( 공무원 / 사학 / 군인 / 별정우체국 ) 간의 연계가 이루어지지 않고 있 어 공적연금의 사각지대가 발생해 노후생활안정 달성 미흡 연계제도 시행전.

Жюль Верн ( ). Я мальчиком мечтал, читая Жюля Верна, Что тени вымысла плоть обретут для нас; Что поплывет судно громадней «Грейт Истерна»; Что.

Solving Algebraic Equations. Equality 3 = = = 7 For what value of x is: x + 4 = 7 true?

4.4 Factoring Quadratic Expressions Learning Target: I can find common binomial factors of quadratic expressions. Success Criteria: I can find the factors.

Factoring Day 1 I can factor a quadratic expression. x 2 + 3x + 2 Rewrite as (x + 1)(x + 2)

Integers: One of the positive or negative numbers I,2,3 Ex: 2+(-6)=-4.

Create a grid. Write one factor (in expanded notation) along the top. Multiply each expanded number in the top factor by each expanded number in the.

♣Multiplying Decimals♣

In this lesson, we will multiply polynomials

Factoring Trinomials 1 February 1, 2017.

Notes Over 10.3 Multiply binomials by using F O I L.

Collecting Like terms Brackets 2 Brackets

= x2 + 10x + 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)

Factoring Special Cases

Multiplication using the grid method.

Multiplying Polynomials Using Algebra Tiles

Warm-Up Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Divide the number in C by 10.

How to Multiply using Lattice

Completing the Square.

9.2 - Multiplying Polynomials

Presentation transcript:

Multiplying Binomials using the Grid Method Feb S. Calahan

The problem: (x + 3)(x + 2)  Set up the first expression on the top of the grid.  x + 3

Step 2: Place the second expression on the side. x + 3  x + 2

Multiply by the top x x + 3 x + 2 (x)(x) 2x

Multiply by 3 x + 3 x + 2 x2x2 3x 2x6

Add like terms  Our answer would look like this x 2 + 2x + 3x +6 = x 2 + 5x + 6

Try another one. (x – 4)(x + 4) X - 4 X + 4

Multiply by the top x X - 4 X + 4 x2x2 4x

Multiply by -4 X - 4 X x -16 x2x2 4x

Write the answer X 2 +4x -4x -16 X