Multiplying a Monomial by a Polynomial Flashcards

Comprehensive vocabulary and property study set covering the multiplication of monomials by polynomials based on lesson rules and examples.

Product sign rule (Same signs)

The rule stating that the product of two factors with the same sign is positive.

Product sign rule (Different signs)

The rule stating that the product of two factors with different signs is negative.

Laws of exponents (Product rule)

If $a$ is any variable and $m$ and $n$ are positive integers, then $a^m \times a^n = a^{m+n}$.

Multiplication of $3xy^2 \times (-4x^3y)$

A process involving sign rules and exponent laws that results in $-12x^4y^3$.

Distributive property (Monomial by Binomial)

The property used to multiply a monomial by a binomial, expressed as $a \times (b + c) = a \times b + a \times c$.

Product of $4a \times (5a + 6)$

The result calculated using the distributive property: $4a \times 5a + 4a \times 6 = 20a^2 + 24a$.

General Distributive property

The principle used to multiply a monomial by any polynomial, expressed as $a \times (b + c + d \text{...}) = a \times b + a \times c + a \times d \text{...}$.

Product of $3a \times (3a^2 - 2a + 2)$

The result calculated using the distributive property: $3a \times 3a^2 + 3a \times (-2a) + 3a \times 2 = 9a^3 - 6a^2 + 6a$.