Algebraic Simplification: Addition, Subtraction, and Multiplication of Algebraic Terms

Algebraic Simplification: Addition, Subtraction, and Multiplication of Algebraic Terms

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Interactive Video

Mathematics

University

Hard

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The video tutorial covers algebraic operations on functions, including addition, subtraction, and multiplication. It begins with an introduction to two functions, F(x) and G(x), and demonstrates how to perform various operations on them. The tutorial explains multiplying a function by a term, adding and subtracting functions, and multiplying two functions together. Each operation is detailed with step-by-step instructions, emphasizing the importance of collecting like terms and handling negative signs. The tutorial concludes with a verification of results using substitution to ensure accuracy.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the two functions introduced in the video?

F(x) = 5X^2 - 3X + 4 and G(x) = 4X^2 + 2X - 5

F(x) = 2X^3 - 4X + 5 and G(x) = 3X^3 + 2X - 6

F(x) = 3X^2 + 2X - 4 and G(x) = 6X^2 - 3X + 5

F(x) = 4 - 2X + 3X^3 and G(x) = 5 - 3X + 6X^3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of multiplying G(x) by -3X?

-15X^3 + 9X^2 - 18X

-15X + 9X^3 - 18X^2

-15X^2 + 9X - 18X^3

-15X + 9X^2 - 18X^4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of adding the functions F(x) and G(x)?

9 - 5X^2 + 9X

9 - 5X + 9X^3

9X^3 - 5X + 9

9X^2 - 5X + 9

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of subtracting G(x) from F(x)?

1 - X + 3X^3

1 + X - 3X^3

-1 + X - 3X^3

-1 - X + 3X^3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in multiplying the functions F(x) and G(x)?

Divide each term in F(x) by each term in G(x)

Subtract the coefficients of like terms

Add the coefficients of like terms

Multiply each term in F(x) by each term in G(x)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of multiplying the functions F(x) and G(x)?

20 - 22X^2 + 6X^3 + 39X^4 - 21X^6 + 18

20X^3 - 22X^2 + 6X + 39 - 21X^4 + 18X^6

20X^6 - 22X^4 + 6X^3 + 39X^2 - 21X + 18

20 - 22X + 6X^2 + 39X^3 - 21X^4 + 18X^6

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can you verify the result of multiplying F(x) and G(x)?

Substitute X = 1 into both functions and check if the result is 40

Substitute X = -1 into both functions and check if the result is -40

Substitute X = 0 into both functions and check if the result is 0

Substitute X = 2 into both functions and check if the result is 80

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