alge-tiles expanding binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

Alge- Tiles Expanding Binomials

Upload: tobias-horton

Post on 04-Jan-2016

239 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

Alge-TilesExpandingBinomials

1–x

–x2

–1

1 –1 = 0x

–x = 0

–x2x2 = 0

Page 3: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

x2 + 5x + 4

1) Expandx

+ 1

x + 4

(x + 4)(x + 1)

Form a rectangle

x x x x

x2 + 6x + 9

2) Expand

x +

x + 3

(x + 3)2

Form a rectangle

= (x + 3)(x + 3)

x x x

xxx

Page 5: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

x2 – 5x + 6

3) Expand

x –

x – 3

(x – 3)(x – 2)

Form a rectangle

x x x

Page 6: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

2x2 + x – 6

4) Expandx

+ 2

2x – 3

(2x – 3)(x + 2)

Form a rectangle

x x x

Page 7: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

x2 – 4

5) Expand

x –

x + 2

Form a rectangle

(x + 2)(x – 2)

x x

4x2 – 4x + 1

6) Expand2x

– 1

2x – 1

(2x – 1)2

Form a rectangle

X XX

= (2x – 1)(2x – 1)

x2 x2

Standard Form of a Quadratic Relation

y = a(x – s)(x – t) factored form

y = ax2 + bx + c standard form(expanded form)

Example: Expand these expressions

1. (x + 4)(x – 6) Use the distributive property

= x2

= x2 – 2x – 24

+ 4x Collect like terms– 6x – 24

Page 10: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

2. – 3(m – 2n)(m + 8n)

= – 3m2 – 18mn + 48n2

Multiply the brackets, then multiply by – 3

Expand and simplify

= – 3[(m – 2n)(m + 8n)]

= – 3[ m2 + 8mn – 2mn – 16n2]

= – 3[ m2 + 6mn – 16n2]

Page 11: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

Determine the expanded form of the equation of the parabola.

y = a(x – s)(x – t)

y = a(x + 1)(x – 3)

4 = a(1 + 1)(1 – 3)

4 = a(2)(– 2)

4 = a(– 4)

– 1 = a

y = – (x + 1)(x – 3)

Page 12: Alge-Tiles Expanding Binomials. x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

y = – (x + 1)(x – 3)

y = – [(x + 1)(x – 3)]

y = – [x2 – 3x + x – 3)]

y = – [x2 – 2x – 3)]

y = – x2 + 2x + 3

What is the result when you multiply (x+3)(x+2)? x2x2 xxx x x x + 3 x+2x+2 Using algebra tiles, we have The resulting trinomial is x2 x2 + 5x + 6. Notice

2.1 IntroductiontoFunctionsmsenux2.redwoods.edu/IntAlgText/chapter2/section1.pdf · Indeed, if we remind ourselves that the notation f(x) = x2 −2xisequivalenttothenotationf: x−→x2

REVIEW OF ALGEBRA - cheat-sheets.org · 2x2 7x 4 2x 1 x 4 2x r x s rs 4 x2 1 2x2 7x 4 x2 5x 24 x 3 x 8 5 24 3 8 x2 5x 24 r and s r s b rs c x r x s x2 r s x rs x2 bx c 3x(x-2)=3x@-6x

9. x2-2x-35>0 ears) -2x2-48 > 20x 12. 15. x2-x-12>0 -x2-30 > - 18. -l … · 2016-11-17 · 9. x2-2x-35>0 ears) -2x2-48 > 20x 12. 15. x2-x-12>0 -x2-30 > -

superior cabinets price list ... - Mastercraft Kitchens · BD90 720 x 900 x 570mm drawer-line base unit £105.00 570 x 445mm door (x2) ,140 x 445mm dwr (x2) BD100 720 x 1000 x 570mm

Multiplying Binomials Maze - manor alternative placement · 2018-10-17 · x2-3x-40 (x-4)(x-9) (x-5)(x+6) x 2+x-30 (x-10)(x+3) (x-1)(x-7) x 2-2x-1 x2-13x+36 x+7x+30 x 2 +7x+7 X2+9x+7

Chapter 5 Analytic Trigonometry - WordPress.com211 - cos x2 sin x11 - cos x2 sin x 1 - cos x + 1 - cos x sin x = sin2 x + 11 - cos x22 sin x11 - cos x2 cos2 x sin x cos x = cos x sin

400-350= = SOLUTION Weareestimating...5x4 42x 36. G2+x2)3dx SOLUTION Letu =x +x2.Thendu = (5x4 +2x)dx.Hence [ze _lJı = dU = - (x +x2)3 u3 2 u2 2 (x x2)2 37. fe+8)dx SOLUTION Letu

Animation = Interpolations. 2 Interpolations/Régularisations Functions de bases –X(u) = B 0 (u) X 0 + B 1 (u) X 1 + B 2 (u) X 2 + … X0X0 X1X1 X2X2 X3X3

QUADRATICS ax 2 + bx + c. MULTIPLYING BRACKETS (FOIL) x 2 +5x +6 Outside ( x+ 3)(x + 2) First x2x2 Inside Last +2x+3x +6

power integrals - uni-marburg.de · x3 +x2 +x+1 x2 = 1 2 x2 +x− 1 x +logx Z dx ... rational integrals substitution Z dx x x2 −1 3 = 1 8 x2 −1 4 Z dx x2 ... dx 1 x2 +x+1 = 2

Sigma function of y3=x2(x-b1)(x-b2) Branched Coverings

x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

Alge-Tiles an Overview. x x2x2 y y2y2 xy 1 Set 1 Set 2

The Belt Railway Company of Chicago - Multimodalways · 12,000 YARD YARD 2 MT 3 MT 2 MT I J J X2 J Y X I J X X I J X2 X I J X2 X2 I T X I J X Y I J X2 ... Argo Industrial and West

Activité Mentale - Sésamath...Question no 4 Calculer : f(x)+5 avec x =3 et f(x)=x2 +1 f(x +5) avec x =3 et f(x)=x2 +1 Activité Mentale 30

T 4 X raining for ExcEllEncE c EaTiv r 4 · 2018-01-24 · T 4 X T r raining T 4 X2 T 4 X2 T 4 X2 T 4 X2 T 4 X2 T 4 X2 T 4 X2 T 4 X2 In der Tradition von T 4 X2 T 4 X2 T 4 X2 T 4

Animation: Interpolations. 2 Interpolations/Régularisations Functions de bases –X(u) = B 0 (u) X 0 + B 1 (u) X 1 + B 2 (u) X 2 + … X0X0 X1X1 X2X2 X3X3

webrx-reactx1, x2, x3) => ({ x1, x2, x3 }), ) // { x1, x2-0, x3-0 } .subscribe(x => { console.log(JSON.stringify(x)); }); React Rendering Engine Readonly Component Attributes Readonly

Formalizingthe p-adicNumbers inLean · Therationalnumbers TherationalnumbersQareincomplete. Thesets x 2Q x2 2 partitionQ,butbothareopen. Alternatively: thesequenceofrationals

Algebra II Factoring #2 Trinomials · !1.! x2+4x+3!26.! x2–3x–10!!2.! x2–4x+3!27.! x2+3x–1!3.! x2–2x–3!28.! x2–x–30!4.! x2+2x–3!29.! x2–17x+30!5.! x2+8x+7!30.!

Resolucion gr´ aﬁca de problemas de´ optimizacion´ · Resolucion´ graﬁca´ Un problema de optimizacion´ Opt. x +3y s.a x2 +y2 16 y x2 y x 2 x 0 x = 0 x2 +y2 = 16 Para resolver

sites.wcsu.edu€¦ · Fundamental Theorem of Algebra (Examples) Consider: x4 9 = (x2 3)(x2 +3) = (x p 3)(x + p 3)(x2 +3) = (x p 3)(x + p 3)(x i p 3)(x +i p 3) This could be partially

HRSB, 2008 Algebra Tiles 1 x -x x2x2 -x 2. HRSB, 2008 Algebra Tiles y-y xy -y 2 y2y2 -xy

PS202 x2 1 PS203 x4 LA021 x 1 PS204 x2 2 FN039 x6 ......FS109 (M8 x 90) x2 FS105 (M8 x 55) x2 FW021 (M8) x2 FN039 (M8) x6 FS110 (M8 x 10) x2 FS103 (M6 x 25) x2 PS201 x2 PS202 x2 PS203

Questions for Week 1 - University of Western Australia€¦ · Web viewBig O Notation Group the following functions into equivalent Big-Oh functions: x2, x, x2 + x, x2 − x, and

a bi i x 2 x2 x

ADDERLINK X Series X2-Silver & X2-Silver Dual Access · 2011-11-29 · ADDERLINK X Series X2-Silver & X2-Silver Dual Access Keyboard, video, mouse and RS232 extender giving sharp,

f(x) = x2 + 8x - Weebly...f(x) = x2 + 8x + 15, g(x) = 5 determine the following: Advanced Algebra 14.1 Practice 15, h(x) = x2 — 9, and 8Ä-15 x-3 X+5 -3 X-IS —05 s) 710 Given the

· Question 11: xx2-3 + (x — 3) x2 for x > 3. Answer 11: and v = (x — 3)x2 therefore, y = Letu = Differentiating with respect to x, we have dy du dv dx dx dx x2-3 taking log

michaelbor.github.iomichaelbor.github.io/presentation_podc2011.pdf · So, Why Algebraic Gossip is Faster? 4/12 A B Pr(helpful) = 1 k [x 1;x2;x 3;:::xk] [x ;x2=?;x ;:::xk] Without

Name: Find the limit. Date - STATEXT: Easy Statistics · Name: Find the limit. Date: 17.lim x!1 x 1 x2 4x+3 18.lim x! 3 x+3 x2 +8x+15 19.lim x!2 x2 3x+2 x2 +x 6 20.lim x!4 x 4 x2

1.8 Combinations of Functions: Composite Functions. 84-92.pdf · f g x f x g x 2x 1 x2 2x 1 x2 4x f x 2x 1 g x x2 2x 1, f g x. ... Sum, Difference, Product, and Quotient of Functions

Symmetry Operations brief remark about the general role of symmetry in modern physics V(X) x V(X 1 ) X1X1 V(X 2 ) X2X2 change of momentum V(X) x conservation