Algebra: Multiplying by a Monomial Flashcards

What is the base in an exponential expression?

What does the exponent in an exponential expression indicate?

What is a polynomial?

What is the result of the product -a^2b^2c^2(a + b - c)?

What do you get when you simplify 8y(y - 4) + 3y(y + 2)?

What is the result of simplifying p(p - q) - q(q - p)?

What do you get when you simplify 8 + 3{x - 2[x + 5(x + 3)]}?

What is the product of 3a^2 and 2a^3?

What do you get when you simplify 7(n - p) + 5p?

What is the product of -2xa(-4xb - 2x^3 + 5x)?

What is the product of 2y^2(3x + 5z)?

What do you get when you find the product of a^4(3a^2 - 2a + 1)?

What is the product of 3(m + n)?

What do you get from -1/2y(2y^3 - 8)?

What is the product of 4xy and y^2 + 2x?

What is the product of -7(8 + k)?

What do you get when you find the product of -4x^3y^2(7xy^4)?

What do you get from simplifying 1/4(8m - 4n) + 1/3(6m + 3n)?

What is the product of x^3(x^2 + 5x + 1)?

What is the method for multiplying monomials?

Key Definitions

Base: The repeated factor in an exponential expression.
Exponent: The superscript number indicating how many times the base is multiplied by itself.
Monomial: A polynomial consisting of a single term.
Polynomial: A mathematical expression composed of one or more terms with whole number exponents.

Examples of Products

Product Calculation: For (-a^2b^2c^2(a + b - c)), the result is (-a^3b^2c^2 - a^2b^3c^2 + a^2b^2c^3).
Simplification Example: (8y(y - 4) + 3y(y + 2)) simplifies to (11y^2 - 26y).

Algebraic Expressions Simplified

For (p(p - q) - q(q - p)), the simplified form is (p^2 - q^2).
Simplifying (8 + 3{x - 2[x + 5(x + 3)]}) leads to (-33x - 82).

Product Finding

For (3a^2 · 2a^3), the product is (6a^5).
The product of (7(n - p) + 5p) results in (7n - 2p).

Multiplying with Variables

Multiplying (-2xa(-4xb - 2x^3 + 5x)) yields (8x^{a+b} + 4x^{a+3} - 10x^{a+1}).
The expression (2y^2(3x + 5z)) results in (6xy^2 + 10y^2z).

Additional Product Examples

For (a^4(3a^2 - 2a + 1)), the product is (3a^6 - 2a^5 + 1a^4).
The product (3(m + n)) simplifies to (3m + 3n).
The expression (-\frac{1}{2}y(2y^3 - 8)) simplifies to (-y^4 + 4y).

Summarizing Multiplication

The product of (4xy) and (y^2 + 2x) results in (4xy^3 + 8x^2y).
Simplifying (-7(8 + k)) gives (-7k - 56).
For (-4x^3y^2(7xy^4)), the simplified product is (-28x^4y^6).

Final Simplifications

The expression (\frac{1}{4}(8m - 4n) + \frac{1}{3}(6m + 3n)) simplifies to (4m).
Finding the product (x^3(x^2 + 5x + 1)) results in (x^5 + 5x^4 + x^3).

Review of Key Concepts

To multiply monomials, multiply coefficients and like bases.
Distribute monomials across polynomials with multiple terms.
Simplification involves removing grouping symbols through distribution and combining like terms.

Test your knowledge on important algebraic terms with these flashcards focused on multiplying by a monomial. Learn the definitions of key concepts like base, exponent, monomial, and polynomial. Perfect for quick reviews and enhancing your understanding of algebra basics.