What is a;ways the sign of the first term and the last term in the product when the binomial is squared?

Question

Could you explain how you got this answer?

Answer 1

the first and last terms of the square of a polynomial will always have a positive sign, and not be negative.

Thats because when you multiply polynomials, the first term ofthe result is the product of the first terms of the polynomials, and the last tem is the product of the last terms of the polynomials.

When you square a polynomial, the first term of the result will be the square of the first term of the polynomial, and the last term of the result will be the square of the last term of the polynomial.

Since the square of any number (positive or negative) is always a positive number, you can be assured that when you square a polynomial, the first and last terms will have positive sign.

Answer 2

Positive.

Let A+B be our binomial.
(A+B)^2 = (A+B)(A+B)
(A+B)(A+B)=A(A+B)+B(A+B)
A(A+B)+B(A+B)=A^2+AB+BA+B^2
AB=BA (reflexive property of equalities)
A^2+AB+BA+B^2=A^2+2AB+B^2
(A+B)^2=A^2+2AB+B^2 (tranistive property)

Regardles of sign, if a real number is squared, the product is positive. Imaginary numbers squared are negative.

So, the sign if the first and third term will always be positive for real numbers. They will always be negative for imaginary numbers.

Answer 3

The sign is always plus (+), because if you multiply a plus times a plus, you get a plus, and if you multiply a minus times a minus, you still get a plus.