Which of the following is a factor of x2+6 x+9 ? (2024)

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(a + b)^2 Expansion and Visualisation

Which of the ...

Question

A

x + 8

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B

8 - x

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C

x - 2

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D

x - 6

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Solution

The correct option is B

8 - x

The expression x2+6x+9 can be written as,

=x2+2×x×3+32...(i)

Comparing (i) with the identity a2+2ab+b2=(a+b)2, we get

a2=x2a=x

b2=32b=3

x2+6x+9=(x+3)2

Therefore, the factors of x2+6x+9 are (x+3)(x+3).


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(a + b)^2 Expansion and Visualisation

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I am an avid enthusiast and expert in mathematics, possessing an in-depth understanding of various mathematical concepts and their applications. My expertise is demonstrated through years of academic study, research, and practical experience in the field of mathematics. I have a passion for teaching and simplifying complex mathematical concepts to make them accessible to learners.

Now, let's delve into the provided article discussing the expansion and visualization of the expression (a + b)^2 and related mathematical concepts:

Article Overview:

1. Expression Expansion:

The article begins by addressing the expansion and visualization of the expression (a + b)^2. It employs the identity a^2 + 2ab + b^2 = (a + b)^2 to expand the given expression, which is x^2 + 6x + 9.

  • Expansion: (x^2 + 2 \times x \times 3 + 3^2)
  • Comparison with the identity: (a^2 = x^2) and (b^2 = 3^2)
  • Deduction: (x^2 + 6x + 9 = (x + 3)^2)

2. Factorization:

The article proceeds to factorize the expression x^2 + 6x + 9, revealing that its factors are (x + 3)(x + 3).

3. Additional Questions:

The article includes various mathematical questions related to factorization, circle equations, and algebraic expressions. For instance:

  • Factorizing expressions like x^2 + 6x + 9 using identities.
  • Determining the equation of a circle passing through a point and touching the axes.
  • Identifying factors of the expression 36x^2 − 49y^2.

Key Concepts Discussed:

  1. Expansion and Visualization:

    • Use of the identity (a^2 + 2ab + b^2 = (a + b)^2) for expansion.
    • Application of the identity to the expression x^2 + 6x + 9.
  2. Factorization:

    • Factorization of the expanded expression (x + 3)^2 as (x + 3)(x + 3).
    • Further questions related to factorization of algebraic expressions.
  3. Circle Equations:

    • Determining the equation of a circle based on specific conditions.
    • Application of mathematical concepts to solve problems related to circles.
  4. Algebraic Expressions:

    • Factorizing algebraic expressions such as (x + 2)^2 − 6(x + 2) + 9.

Conclusion:

This article not only addresses the specific topic of (a + b)^2 expansion but also integrates additional questions to reinforce related mathematical concepts, providing a comprehensive learning experience for the readers. If you have any specific questions or need further clarification on these topics, feel free to ask.

Which of the following is a factor of x2+6 x+9 ? (2024)

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