Algebra Class: Expressions and Identities
8 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the area of a rectangle that is 2 units wide and 3 units long?

6

What is the formula for the area of a rectangle?

length * width

The area of a ______ is found by multiplying its length and width.

rectangle

What is the formula for the volume of a rectangular prism?

<p>length * width * height</p> Signup and view all the answers

What is the volume of a rectangular prism with a width of 3 units, a length of 4 units and a height of 5 units?

<p>60</p> Signup and view all the answers

What is the volume of a rectangular prism that is 2 units wide, 3 units long, and 4 units high?

<p>24</p> Signup and view all the answers

The volume of a rectangular ______ is found by multiplying its length, width, and height.

<p>prism</p> Signup and view all the answers

What is the product of 4x and 3y?

<p>12xy</p> Signup and view all the answers

Flashcards

What is an algebraic expression?

An expression made up of variables, constants, and mathematical operations. It does not have an equal sign.

What are like terms?

Terms within an algebraic expression that have the same variable and exponent. For example: 3x^2 and -5x^2 are like terms.

How do you add or subtract algebraic expressions?

Adding or subtracting algebraic expressions involves combining like terms. For example: (2x + 3y) + (4x - y) = 6x + 2y.

What is a monomial?

A monomial is an algebraic expression with only one term. For example: 5x, 7y^2, -3ab.

Signup and view all the flashcards

What is a binomial?

A binomial is an algebraic expression with two terms. For example: 2x + 3, a^2 - 4b.

Signup and view all the flashcards

What is a trinomial?

A trinomial is an algebraic expression with three terms. For example: x^2 + 2x - 1, 3a^2 - 2ab + b^2.

Signup and view all the flashcards

What is a polynomial?

A polynomial is an algebraic expression with one or more terms, where the exponents are non-negative integers. It can be a monomial, binomial, trinomial, or more.

Signup and view all the flashcards

How do you multiply two monomials?

Multiplying two monomials together involves multiplying the coefficients and adding the exponents of the like variables. For example: (4x^2) * (3x) = 12x^3.

Signup and view all the flashcards

How do you multiply a monomial by a polynomial?

Multiplying a monomial by a polynomial involves multiplying the monomial by each term of the polynomial. For example: 2x * (3x + 5) = 6x^2 + 10x.

Signup and view all the flashcards

How do you multiply two binomials?

To multiply two binomials, use the FOIL method (First, Outer, Inner, Last). This means multiplying the first terms, outer terms, inner terms, and last terms of each binomial and then combining like terms. For example: (x + 2) * (x + 3) = x^2 + 5x + 6.

Signup and view all the flashcards

How do you multiply a binomial by a trinomial?

Multiplying a binomial by a trinomial works similarly to multiplying a binomial by a binomial, but you have to multiply each term in the binomial by each term in the trinomial and then combine like terms. For example: (x + y) * (x^2 + 2xy + y^2) = x^3 + 3x^2y + 3xy^2 + y^3.

Signup and view all the flashcards

Study Notes

Algebraic Expressions and Identities

  • Algebraic expressions are combinations of variables, constants, and mathematical operations.
  • Examples include: x + 3, 2y – 5, 3x², 4xy + 7.
  • Addition and subtraction of algebraic expressions involve combining like terms. Like terms have the same variables raised to the same power.
  • Observe the coefficients and add (or subtract) them to combine like terms.
  • Example: 7x² – 4x + 5 + 9x – 10 = 7x² + 5x – 5

Multiplication of Algebraic Expressions

  • Multiplying algebraic expressions involves multiplying coefficients and variables.
  • When multiplying variables, add the exponents of the same variables.
  • An expression with one term is a monomial, two terms is a binomial, and three terms is a trinomial, and many terms is a polynomial.
  • Example: 5x × 4x² = 20x³
  • More complex products follow the distributive property: 3x(5y + 2) = (3x × 5y) + (3x × 2) = 15xy + 6x.

Multiplying a Monomial by a Polynomial

  • Involves multiplying the monomial by each term of the polynomial.
  • Use the distributive property.
  • Combine like terms.
  • Example: 3x(4x² + 5x + 7) = (3x × 4x²) + (3x × 5x) + (3x × 7) = 12x³ + 15x² + 21x

Multiplying a Binomial by a Binomial

  • Use the distributive property to multiply each term of the first binomial by each term of the second.
  • Combine like terms.
  • Example: (x - 4)(2x + 3) = x(2x + 3) – 4(2x + 3) = 2x² + 3x – 8x – 12 = 2x² - 5x - 12

Volume

  • Volume is calculated by multiplying length × breadth × height.
  • Example: Volume of a rectangular box with length 2ax, breadth 3by, and height 5cz is 2ax × 3by × 5cz = 30abcxyz.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Algebraic Expressions and Identities PDF

Description

This quiz covers the basics of algebraic expressions and identities, including how to combine like terms and multiply expressions. Gain a solid understanding of monomials, binomials, trinomials, and polynomials, as well as the distributive property. Perfect for reviewing key concepts in algebra.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser