8.3 Mult.Bionmials.Notes PDF Section 8-3: Multiplication of

Reteaching - 8-3

You can multiply binomials by using the FOIL method. FOIL stands for First. Outer

Reteaching

Reteach 8-3. Name: 8-3. Reteaching. You can multiply binomials by using the FOIL method. FOIL stands for First. Outer

( 4 )x J ( 4 )5

26-Dec-2005 Use the Distributive Property to multiply binomials and polynomials. ... X(2x² + 4x+8) + 3 (2x² + 4x+8). 2x²+10x² + 20x + 24 x² - 49 x² + 3x + ...

Reteach 11-8

Use FOIL to multiply binomials with square roots. Multiply 3 2 4 2 . ( 3 V2 )( perimeter: 8 r. ^. 3 m. A. TABLE. 28 10 in. 8 6 in. 448 r. ^. 15 i n 2. ADDITION^.

Reteaching - 8-7

Some binomials are a difference of two squares. To factor these expressions Multiply to check your answer. (2x 1 3)(2x 2 3) 5 4x2 1 6x 2 6x 2 9. 5 4x2 2 ...

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Lesson 9-3 Multiplying Binomials. 507. 12n3 – 10n2 ± 34n – 56. 35. 13 x2 ± 2x 8. 7m3 ± 27m2 – 6m. 9. d5 – 4d3 – 18d2 pages 507–510 Exercises. 5. x2 ± 7x ± 10.

( 4 )x J ( 4 )5

26-Dec-2005 Use the Distributive Property to multiply binomials and polynomials. ... X(2x² + 4x+8) + 3 (2x² + 4x+8). 2x²+10x² + 20x + 24 x² - 49 x² + 3x + ...

Reteaching - 8-6

7x2 1 31x 1 12 5 (7x 1. )(x 1. ) The trinomial has two plus signs so the binomials also have plus signs. Because c is 12

Reteaching - 8-8

5 x(6x 2 5)(2x 1 3). 2x 1 3 is the common binomial term. Use the. Distributive Property to reorganize the factors. Multiply to check your answer. x(6x 2 5)(2x 1

Review - Zen-Math with Dr. Wade

8-3. Reteaching (continued). Multiplying Binomials. 2x2 ? 2 5 4x2. 3x ? 2 5 6x. 24 ? 2 8-8. Reteaching. Factoring by Grouping. You can factor some higher- ...

Reteaching - 8-3

You can multiply binomials by using the FOIL method. 8-3. Reteaching. Multiplying Binomials a2 1 3a 2 18. 6d2 1 8d 2 8. 5g2 2 12g 2 9 b2 1 b 2 20.

Practice

23. (4m - 1)(m + 4). 24. (7z + 3)(4z - 6). 25. (2h + 6)(5h - 3). 26. (3w + 12)(w + 3). 27. (6c - 2)(9c - 8). Practice. Form G. Multiplying Binomials.

Review

8. 5e2(–3e2 – 2e – 3). 9. 4f(–3f3 + 2f2 + 6). Multiplying and Factoring. Problem 8-3. Review. You can multiply binomials by using the FOIL method.

8.3 Mult.Bionmials.Notes

Section 8-3: Multiplication of Binomials Multiply 2x(5x + 8) + 3(5x + 8). 10x2 + 16x + 15x + 24 ... Multiply A Binomial by a Trinomial:.

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3. 7.15x-x²³ +3. 8. 5x + 2x²-x + 3x². 9. 9x³. -X³+15X +3. 3x² + 2x² + 4x 8-3. Multiplying Binomials. Simplify each product using the Distributive ...

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8. (3x + 2)(3x + 2). 11. (4x + 1)(2x ? 1). BGQ. Lesson 9-3 Reteaching. 1000 000-0000000. Multiplying Binomials. 9). 3. (x-3)(x +. 6. (x + 4)(2x + 5).

Practice

8-3. Practice. Form K. Multiplying Binomials. Simplify each product using the Distributive Property. 1. (b J 2)(b + 1). 2. (x + 6)(x + 5). 3. (3n + 1)(n J 8

Binomial Squares and Other Special Products

This problem asks us to find the square of a binomial. Solution: Examples: Multiply using the FOIL method. 8. (2x – 3)(2x + 3).

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The denominator is 8 so the divisor is 8. So = 58. So 3 8 = 3. Write a division expression for each fraction.

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Lesson 9-3 Multiplying Binomials. 505. Multiplying Binomials. Part 1 Multiplying Two Binomials. You can use an area model to multiply two binomials.

Multiplying Binomials - Math Men

Reteaching 8-3 Multiplying Binomials You can multiply binomials by using the FOIL method FOIL stands for First Outer Inner and Last Problem What is the simplifi ed form of (4x 3)(2x 6)? 1 Use the FOIL method to simplify the binomial Solve x 4 x x2 2 5 8 Multiply the First terms x x 4 ? 6 5 24 Multiply the Outer terms x x 3 ? 2 5 6

Multiplying Binomials - Math Men

8-3 Practice Form K Multiplying Binomials Simplify each product using the Distributive Property 1 (b2 2)(b1 1) 2 (x1 6)(x1 5) 3 (3n1 1)(n2 8) 4 (2t2 7)(t2 5) 5 (y1 3)(y1 7) 6 (b2 6)(b1 3) Simplify each product using a table 7 (x1 1)(x2 11) 8 (h2 2)(3h1 5) 9 (8w2 3)(4w2 7) 10 (3c1 13)(13c1 3) 11 (3a1 2)(a2 2) 12 (t1 7)(2t2 4) 13

0022 hsm11a1 te 0803tr - Math Men

8-3 Reteaching You can multiply binomials by using the FOIL method FOIL stands for First Outer Inner and Last What is the simplified form of (4x + 3)(2x + 6)? Use the FOIL method to simplify the binomial Solve 4x · 2x = 8x2 Multiply the First terms 4x · 6 = 24x Multiply the Outer terms 3 · 2x = 6x Multiply the Inner terms 3 · 6

Searches related to 8 3 reteaching multiplying binomials

The term FOIL is a memory device for applying the Distributive Property to the product of two binomials EXAMPLE 1: MULTIPLYING USING FOIL Simplify 1 2 3 4 5 6 7 8 9 10 11 12 (3x+4)(2x+5)(3x?4)(2x+5)(3x+4)(2x?5)(3x?4)(2x?5) (4x+2)(3x?1)(6x?5)(3x+1)(3x?4)(3x+1)(3x+4)(3x?4) (d+9)(d?11)(b+3)(2b?5)(2x?5)(x?4)(2x

Section 8-3:Multiplication of Binomials

Objective:to multiply polynomials by using the distributive property, the FOIL method, the Box method, or the vertical method

There are 4techniques you can use for multiplying polynomials.1)Distributive Property2)Box Method (Area Model)3)FOIL Method4)Vertical Method

1stMethodDistributive Property

Multiply 2 Binomials:(2x + 3)(5x + 8)Multiply 2x(5x + 8) + 3(5x + 8).10x2+ 16x + 15x + 24Combine like terms.10x2+ 31x + 24

Multiply A Binomial by a Trinomial:(2x -5)(x2-5x + 4)2x(x2-5x + 4) -5(x2-5x + 4)2x3-10x2+ 8x -5x2+ 25x -20Group and combine like terms.2x3-10x2-5x2+ 8x + 25x -202x3-15x2+ 33x -20

Got it? #1 on page 498(x -6)(4x + 3)x(4x + 3) -6(4x + 3)4x2+ 3x -24x -18 Combine like terms.4x2-21x -18

2ndMethodBox Method (Area Model)

This method works for every problem!Here's how you do it. Multiply (3x -5)(5x + 2)Draw a box. Write a polynomial on the top and side of a box. It does not matter which goes where.(Be careful with your signs!)3x-55x+2

Multiply (3x -5)(5x + 2)Combine like terms.15x2-19x -103x-55x+215x2+6x-25x-10 Multiply (7p -2)(3p -4)Combine like terms.21p2-34p + 87p-23p-421p2-28p-6p+8

x2-5x+42x-5Multiply (2x -5)(x2-5x + 4)You cannot use FOIL because they are not BOTH binomials. You must use the distributive property or box method.2x3-5x2-10x2+25x+8x-20Almost done!Go to the next slide!

x2-5x+42x-5Multiply (2x -5)(x2-5x + 4)Combine like terms!2x3-5x2-10x2+25x+8x-202x3-15x2+ 33x -20

Similar to the Box Method is the Area Model.

Got it? #2 on page 499(3x +1)(x + 4)3x2+13x +4

3rdMethodFOIL Method

The FOILmethodis ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply.2) Use the FOIL method to multiply the following binomials:(y + 3)(y + 7)

(y + 3)(y + 7) Ftells you to multiply the FIRSTterms of each binomial.y2 (y + 3)(y + 7) Otells you to multiply the OUTERterms of each binomial.y2+7y (y + 3)(y + 7) Itells you to multiply the INNERterms of each binomial.y2+ 7y +3y

(y + 3)(y + 7) Ltells you to multiply the LASTterms of each binomial.y2+ 7y + 3y+ 21Combine like terms.y2+ 10y + 21

Remember, FOIL reminds you to multiply the:First termsOuter termsInner termsLast terms Got it? #3 on page 500A)3x2+ 2x -8 B)4n2-31n + 42 C)4p3-10p2 + 6p -15 Review Problem #4 on page 500Got it? #4 on page 5004πx2+ 20πx+ 24π

4thMethodVertical Method

Simplify (4x+ 2)(3x-6). Vertical Method4x + 23x -6 x-24x -12 12x2 + 6x 12x2 -18x -12 Multiply each term by -6Multiply each term by 3x

Got it? #5 on page 501A)2x3-9x2 + 10x -3 A)Refer back to earlier example in this Powerpoint

Informally check to make sure you are on the right track:•the problem has 2 terms in the first polynomial and 3 terms in the second polynomial (2 * 3 = 6)•Six is then the number of terms you should have BEFORE you collect like terms and get your final answer

Find the area of the shaded region. Simplify.area of outer rectangle = (3x+ 2)(2x-1)area of hole = x(x+ 3)area of shaded region = area of outer rectangle -area of hole= (3x+ 2)(2x-1) -x(x+ 3)Substitute.= 6x2-3x+ 4x-2 -x2-3xUse FOIL to simplify (3x+ 2) (2x-1) and the Distributive Property to simplify x(x+ 3).= 6x2-x2-3x+ 4x-3x-2Group like terms.= 5x2-2x-2Simplify.Applying Multiplication of Polynomials

Practice1. Simplify the product using the FOIL method. (x + 2)(x + 5)2. Simplify the product using the vertical method. (r + 6)(r -4)3. Simplify using the box method. (-7 + p)(8 + p)4.Use any method to simplify the products (a -4)(a2-2a + 1)5. Simplify (2x + 2)2x2+ 7x + 10r2+ 2r -24 p2+ p -56 a3-6a2+ 9a -44x2+ 8x + 4

Multiply (y + 4)(y -3)1.y2+ y -122.y2-y -123.y2+ 7y -124.y2-7y -125.y2+ y + 126.y2-y + 127.y2+ 7y + 128.y2-7y + 12Try This...

Multiply (y + 4)(y -3)1.y2+ y -122.y2-y -123.y2+ 7y -124.y2-7y -125.y2+ y + 126.y2-y + 127.y2+ 7y + 128.y2-7y + 12

Multiply (2a -3b)(2a + 4b)1.4a2+ 14ab -12b22.4a2-14ab -12b23.4a2+ 8ab -6ba -12b24.4a2+ 2ab -12b25.4a2-2ab -12b2Try Another...

Multiply (2a -3b)(2a + 4b)1.4a2+ 14ab -12b22.4a2-14ab -12b23.4a2+ 8ab -6ba -12b24.4a2+ 2ab -12b25.4a2-2ab -12b2

Multiply (2x +3)(x2+4x+5)1.2x3+ 8x2+10x + 3x2+ 12x +152.2x3+ 11x2+ 22x+153.13x2+ 22x+154.2x3+ 32x+15quotesdbs_dbs5.pdfusesText_9

[PDF] 8.3 Mult.Bionmials.Notes Section 8-3: Multiplication of

Section 8-3:Multiplication of Binomials

1stMethodDistributive Property

2ndMethodBox Method (Area Model)

Similar to the Box Method is the Area Model.

Got it? #2 on page 499(3x +1)(x + 4)3x2+13x +4

3rdMethodFOIL Method

4thMethodVertical Method