Question
Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?
Hint:
A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial.
The methods used to find the product of binomials are called special products.
Difference of squares is a case of a special product which occurs when we multiply a binomial by another binomial with the same terms but the opposite sign.
The correct answer is: a2 - b2
Let’s first the product of (𝑎 + 𝑏) and (𝑎 − 𝑏)
(a + b)(a - b) = a(a - b) + b(a - b)
= a(a) + a(-b) + b(a) + b(-b)
= a2 - ab + ab - b2
= a2 - b2
Final Answer:
The product of (𝑎 + 𝑏) and (𝑎 − 𝑏) is a2 - b2 which has only two terms and hence it is a binomial.
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