Multiplying Polynomials by Monomials Explained

The video tutorial covers Chapter 4, Section 5 on multiplying polynomials by monomials. It begins with an introduction to the concept, followed by several examples demonstrating how to simplify expressions by distributing terms. The tutorial includes examples of distributing 4x squared across multiple terms, multiplying expressions with variables, solving equations to isolate Y, and calculating the area of a shaded portion in a rectangle. Each example is explained step-by-step to enhance understanding.

What operation is performed when multiplying a monomial by a polynomial?

• Subtraction of exponents

• Division of terms

• Distribution across terms

• Multiplication of coefficients only

When multiplying 'y' by 'y', what is the resulting exponent of 'y'?

• 2y

• y^3

• y^2

• y^1

What is the result of multiplying 4x^2 by 5x^2?

• 10x^4

• 20x^2

• 20x^4

• 9x^4

How do you simplify the expression -3 * -a?

• -a

• 3a

• -3a

• 0

What is the simplified form of 2a + 3a?

• 5a^2

• a^2

• 6a

• 5a

What is the result of distributing -3 to the terms 1 and -a?

• -3 - 3a

• -3 + 3a

• 3 - a

• -3a + 1

How do you find the value of 'y' in the equation 0 = 4y - 4 - 3y + 6?

• y = 0

• y = -2

• y = 2

• y = 1

What is the first step in finding the area of the shaded portion?

• Find the area of both rectangles separately

• Multiply the length by the width of the shaded area

• Add the areas of both rectangles

• Subtract the smaller area from the bigger area

What is the area of the bigger rectangle if its length is 3x and width is x+9?

• 3x^2 + 27x

• 3x + 9

• x^2 + 9x

• 3x(x + 3)

What is the final expression for the area of the shaded portion?

• 3x + 23

• x^2 + 9x

• 3x^2 + 27x

• 3x^2 + 23x