Differences of squares

Grade 10s started off today multiplying binomials, and headed towards multiplying a special sort of binomials (ax+b)(ax-b).  Some of us use a box multiplying method, others use a distributive property model with arrows, and others build a model with algebra tiles.

Here’s an example of (2x+3)(2x-3) which simplifies to 4x^2-9.  The -6x and +6x terms cancel out.

We played around with making questions that have only big red squares and small red squares in the expression, (spoiler alert: it isn’t possible, the colours have to be opposite) then we moved to working backwards, and factoring expressions that are made of different coloured squares.

Here’s an example:

We noticed that when the terms are both square numbers, and the signs on the terms are opposite that they can be factored in a special way.  The binomials in the brackets are all the same except one sign will be different.

-36x^2+25=(-6x+5)(6x+5)