Alge-Tiles Expanding Binomials

x x2x2 1 –x–x –x2–x2 –1 1 = 0 x –x–x –x2–x2 x2x2

x 2 + 5x + 4 1) Expand x + 1 x + 4 x2x2 (x + 4)(x + 1) Form a rectangle x x x x x

x 2 + 6x + 9 2) Expand x + 3 x2x2 (x + 3) 2 Form a rectangle = (x + 3)(x + 3) x x x x x x

x 2 – 5x + 6 3) Expand x – 2 x – 3 x2x2 (x – 3)(x – 2) Form a rectangle x x x x x

2x 2 + x – 6 4) Expand x + 2 2x – 3 x2x2 (2x – 3)(x + 2) Form a rectangle x2x2       x x x x x x x

x 2 – 4 5) Expand x – 2 x + 2 x2x2 Form a rectangle (x + 2)(x – 2)     x x x x

4x 2 – 4x + 1 6) Expand 2x – 1 x2x2 (2x – 1) 2 Form a rectangle x2x2 x X X X = (2x – 1)(2x – 1) x2x2 x2x2 x x x 1

Standard Form of a Quadratic Relation y = a(x – s)(x – t)factored form y = ax 2 + bx + cstandard form (expanded form) Example: Expand these expressions 1. (x + 4)(x – 6) Use the distributive property = x 2 = x 2 – 2x – x Collect like terms – 6x– 24

2. – 3(m – 2n)(m + 8n) = – 3m 2 – 18mn + 48n 2 Multiply the brackets, then multiply by – 3 Expand and simplify = – 3[(m – 2n)(m + 8n)] = – 3[ m 2 + 8mn – 2mn – 16n 2 ] = – 3[ m 2 + 6mn – 16n 2 ]

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 2 – 3x + x – 3)] y = – [x 2 – 2x – 3)] y = – x 2 + 2x + 3