Question

3 Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ: ●(a + b)^2, ●(a – b)^2, and ●(a - b)(a + b).

Answer 1

●(a + b)^2 = (a +b) (a +b)

(a + b) (a + b) = a*a + a*b + b*a+ b*b = a^2 + 2ab + b^2

●(a – b)^2 (a - b) (a -b)

(a - b) (a -b) = a*a + -ab - ba + b*b = a^2 - 2ab + b^2

●(a - b)(a + b). =

= (a - b) (a + b) = a*a + ab - ba - b*b = a^2 - b^2