Factorisation Using Algebra Tiles

Transcript

Factorisation Using Algebra Tiles Let’s try to multiply (𝒙+𝟑) and (𝒙+𝟒) We can build a rectangle where Length is 𝑥+3 Width is 𝑥+4 When we multiply them to find the area, we get four distinct zones One massive 𝒙^𝟐 tile Three 𝒙 tiles on the right Four 𝒙 tiles on the bottom A grid of 12 tiny 1 (unit) tiles in the corner Add them all up: 𝑥^2+3𝑥+4𝑥+12=𝒙^𝟐+𝟕𝒙+𝟏𝟐 This figure helps us to visualise two algebraic identities (i) The linear expressions x + 3 and x + 4 can be multiplied to obtain the identity (x + 3)(x + 4) = x2 + 7x + 12. (ii) Also the expression x2 + 7x + 12 can be factored into the linear factors (x + 3) and (x + 4), giving the same identity x2 + 7x + 12 = (x + 3)(x + 4) Let’s do some questions now