Algebra: Multiplying by a Monomial Flashcards

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Questions and Answers

What is the base in an exponential expression?

The number that is repeated as a factor (correct)

The exponent of the expression

A term or a sum of terms

None of the above

What does the exponent in an exponential expression indicate?

The number of times the base is multiplied by itself (correct)

The base of the expression

The product of two numbers

None of the above

What is a monomial?

A one-term polynomial

What is a polynomial?

A term or a sum of terms whose variables have whole number exponents Signup and view all the answers

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

-a^3b^2c^2 - a^2b^3c^2 + a^2b^2c^3 Signup and view all the answers

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

11y^2 - 26y Signup and view all the answers

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

p^2 - q^2 Signup and view all the answers

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

-33x - 82 Signup and view all the answers

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

6a^5 Signup and view all the answers

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

7n - 2p Signup and view all the answers

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

8x^{a+b} + 4x^{a+3} - 10x^{a+1} Signup and view all the answers

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

6xy^2 + 10y^2z Signup and view all the answers

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

3a^6 - 2a^5 + a^4 Signup and view all the answers

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

3m + 3n Signup and view all the answers

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

-y^4 + 4y Signup and view all the answers

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

4xy^3 + 8x^2y Signup and view all the answers

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

-7k - 56 Signup and view all the answers

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

-28x^4y^6 Signup and view all the answers

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

4m Signup and view all the answers

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

x^5 + 5x^4 + x^3 Signup and view all the answers

What is the method for multiplying monomials?

Multiply the coefficients and then multiply like bases. Signup and view all the answers

Study Notes

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.

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Description

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.