Special products
· Special products are products of binomials in special scenarios, which apply to all binomials in that format.
· The special products are:
o (x+y)^2
§ (x+y)^2
§ = (x+y)(x+y)
§ = x(x) + x(y) + x(y) + y(y)
§ = x^2 + 2xy + y^2
Every binomials in (x+y) 2 or (x+y)(x+y) form will result in x^2 + 2xy + y^2 form trinomial.
o (x-y)^2
§ (x-y)^2
§ = (x-y)(x-y)
§ = x(x) + x(-y) - y(x) - y(-y)^2
§ = x^2 – 2xy + y^2
Every binomials in (x-y) 2 or (x-y)(x-y) form will result in x^2 – 2xy + y^2 form trinomial.
o (x+y)(x-y)
§ (x+y)(x-y)
§ = x(x) + x(-y) + y(x) + y(-y)
§ = x^2 – y^2
Every binomials in (x+y)(x-y) form will result in x^2 – y^2 form binomial. When factoring this form, we use difference of squares, which is square rooting each term of the given product.
· The special products are:
o (x+y)^2
§ (x+y)^2
§ = (x+y)(x+y)
§ = x(x) + x(y) + x(y) + y(y)
§ = x^2 + 2xy + y^2
Every binomials in (x+y) 2 or (x+y)(x+y) form will result in x^2 + 2xy + y^2 form trinomial.
o (x-y)^2
§ (x-y)^2
§ = (x-y)(x-y)
§ = x(x) + x(-y) - y(x) - y(-y)^2
§ = x^2 – 2xy + y^2
Every binomials in (x-y) 2 or (x-y)(x-y) form will result in x^2 – 2xy + y^2 form trinomial.
o (x+y)(x-y)
§ (x+y)(x-y)
§ = x(x) + x(-y) + y(x) + y(-y)
§ = x^2 – y^2
Every binomials in (x+y)(x-y) form will result in x^2 – y^2 form binomial. When factoring this form, we use difference of squares, which is square rooting each term of the given product.