Remarkable Products in Algebra

These flashcards cover the rules for calculating the product of conjugate binomials and the square of a binomial based on Chapter 11 notes.

Conjugate binomials are two binomials where one term is __________ and the other term is opposite.

the same

The product of conjugate binomials is calculated by taking the __________ between the square of the same term and the square of the opposite term.

difference

The formula for the product of conjugate binomials is $(A+B)(A-B) = \_\_\_\_\_\_\_\_\_\_$.

$$A^2 - B^2$$

The result of the product of two conjugate binomials is always a(n) __________.

binomial

According to the transcript, when calculating the product of conjugate binomials, it is helpful to mark the term that __________.

changes sign

The square of a binomial results in a(n) __________.

trinomial

If two terms in a binomial have the same sign, the __________ of those terms is positive.

double product

If two terms in a binomial have different signs, the double product of both terms is __________.

negative

The formula for the square of a binomial is $(A+B)^2 = \_\_\_\_\_\_\_\_\_\_$.

$$A^2 + 2AB + B^2$$

To calculate the square of a binomial, you must sum the square of the first term, the double product of both terms, and the __________.

square of the second term

In the example $(2x+5)(2x-5)$, the final result is __________.

$$4x^2 - 25$$

In the example $(2x+5)^2$, the final result is __________.

$$4x^2 + 20x + 25$$

The result of the expression $(-1-10y)^2$ is __________.

$$1 + 20y + 100y^2$$

The result of the expression $(9-3a)^2$ is __________.

$$81 - 54a + 9a^2$$