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

Alge-TilesExpandingBinomials

x

x2

1–x

–x2

–1

1 –1 = 0x

–x = 0

–x2x2 = 0

x2 + 5x + 4

1) Expandx

+ 1

x + 4

x2

(x + 4)(x + 1)

Form a rectangle

x x x x

x

x2 + 6x + 9

2) Expand

x +

3

x + 3

x2

(x + 3)2

Form a rectangle

= (x + 3)(x + 3)

x x x

xxx

x2 – 5x + 6

3) Expand

x –

2

x – 3

x2

(x – 3)(x – 2)

Form a rectangle

x x x

xx

2x2 + x – 6

4) Expandx

+ 2

2x – 3

x2

(2x – 3)(x + 2)

Form a rectangle

x2

x x x

xx

xx

x2 – 4

5) Expand

x –

2

x + 2

x2

Form a rectangle

(x + 2)(x – 2)

x x

xx

4x2 – 4x + 1

6) Expand2x

– 1

2x – 1

x2

(2x – 1)2

Form a rectangle

x2

x

X XX

= (2x – 1)(2x – 1)

x2 x2

x

x

x

1

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

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]

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)

y = – (x + 1)(x – 3)

y = – [(x + 1)(x – 3)]

y = – [x2 – 3x + x – 3)]

y = – [x2 – 2x – 3)]

y = – x2 + 2x + 3