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=x2⇒a=x
b2=32⇒b=3
⇒ x2+6x+9=(x+3)2
Therefore, the factors of x2+6x+9 are (x+3)(x+3).
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=x2⇒a=x
b2=32⇒b=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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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:

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.

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

Circle Equations:
 Determining the equation of a circle based on specific conditions.
 Application of mathematical concepts to solve problems related to circles.

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.