Factor The Expression:$x^2 - 6x + 9$A. $(x-3)^2$ B. $(x+9)^2$ C. $(x+3)^2$ D. $(x-9)^2$

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Introduction

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Factoring an expression is a fundamental concept in algebra that involves expressing a given polynomial as a product of simpler polynomials. In this article, we will focus on factoring the expression $x^2 - 6x + 9$. This expression can be factored using the perfect square trinomial formula, which states that if we have an expression of the form $a^2 - 2ab + b^2$, it can be factored as $(a-b)^2$.

Understanding the Perfect Square Trinomial Formula

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The perfect square trinomial formula is a powerful tool for factoring expressions. It states that if we have an expression of the form $a^2 - 2ab + b^2$, it can be factored as $(a-b)^2$. This formula can be used to factor expressions that have a perfect square trinomial pattern.

Applying the Perfect Square Trinomial Formula

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To factor the expression $x^2 - 6x + 9$, we need to identify the values of $a$ and $b$ in the perfect square trinomial formula. In this case, we can see that $a = x$ and $b = 3$. Therefore, we can rewrite the expression as $(x)^2 - 2(x)(3) + (3)^2$.

Simplifying the Expression

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Now that we have rewritten the expression in the form of the perfect square trinomial formula, we can simplify it by combining like terms. This gives us $(x)^2 - 2(x)(3) + (3)^2 = x^2 - 6x + 9$.

Factoring the Expression

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Now that we have simplified the expression, we can factor it using the perfect square trinomial formula. This gives us $(x-3)^2$.

Conclusion

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In this article, we have shown how to factor the expression $x^2 - 6x + 9$ using the perfect square trinomial formula. We have identified the values of $a$ and $b$ in the formula and rewritten the expression in the form of the formula. We have then simplified the expression and factored it using the formula. The final answer is $(x-3)^2$.

Answer

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The correct answer is A. $(x-3)^2$.

Tips and Tricks

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• When factoring an expression, look for a perfect square trinomial pattern.
• Identify the values of $a$ and $b$ in the perfect square trinomial formula.
• Rewrite the expression in the form of the perfect square trinomial formula.
• Simplify the expression by combining like terms.
• Factor the expression using the perfect square trinomial formula.

Practice Problems

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• Factor the expression $x^2 + 8x + 16$.
• Factor the expression $x^2 - 10x + 25$.
• Factor the expression $x^2 + 6x + 9$.

Conclusion

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Factoring an expression is a fundamental concept in algebra that involves expressing a given polynomial as a product of simpler polynomials. In this article, we have shown how to factor the expression $x^2 - 6x + 9$ using the perfect square trinomial formula. We have identified the values of $a$ and $b$ in the formula and rewritten the expression in the form of the formula. We have then simplified the expression and factored it using the formula. The final answer is $(x-3)^2$.

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Introduction

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In our previous article, we discussed how to factor the expression $x^2 - 6x + 9$ using the perfect square trinomial formula. In this article, we will provide a Q&A guide to help you understand the concept of factoring expressions and how to apply the perfect square trinomial formula.

Q&A

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Q: What is the perfect square trinomial formula?

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A: The perfect square trinomial formula is a powerful tool for factoring expressions. It states that if we have an expression of the form $a^2 - 2ab + b^2$, it can be factored as $(a-b)^2$.

Q: How do I identify the values of $a$ and $b$ in the perfect square trinomial formula?

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A: To identify the values of $a$ and $b$ in the perfect square trinomial formula, you need to look at the expression and identify the values of $a$ and $b$ that fit the pattern. In the expression $x^2 - 6x + 9$, we can see that $a = x$ and $b = 3$.

Q: How do I rewrite the expression in the form of the perfect square trinomial formula?

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A: To rewrite the expression in the form of the perfect square trinomial formula, you need to identify the values of $a$ and $b$ and rewrite the expression as $(a-b)^2$. In the expression $x^2 - 6x + 9$, we can rewrite it as $(x-3)^2$.

Q: How do I simplify the expression?

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A: To simplify the expression, you need to combine like terms. In the expression $(x-3)^2$, we can simplify it by combining the like terms to get $x^2 - 6x + 9$.

Q: How do I factor the expression using the perfect square trinomial formula?

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A: To factor the expression using the perfect square trinomial formula, you need to identify the values of $a$ and $b$ and rewrite the expression as $(a-b)^2$. In the expression $x^2 - 6x + 9$, we can factor it as $(x-3)^2$.

Q: What are some common mistakes to avoid when factoring expressions?

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A: Some common mistakes to avoid when factoring expressions include:

• Not identifying the values of $a$ and $b$ correctly
• Not rewriting the expression in the form of the perfect square trinomial formula
• Not simplifying the expression correctly
• Not factoring the expression using the perfect square trinomial formula

Tips and Tricks

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• When factoring an expression, look for a perfect square trinomial pattern.
• Identify the values of $a$ and $b$ in the perfect square trinomial formula.
• Rewrite the expression in the form of the perfect square trinomial formula.
• Simplify the expression by combining like terms.
• Factor the expression using the perfect square trinomial formula.

Practice Problems

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• Factor the expression $x^2 + 8x + 16$.
• Factor the expression $x^2 - 10x + 25$.
• Factor the expression $x^2 + 6x + 9$.

Conclusion

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Factoring an expression is a fundamental concept in algebra that involves expressing a given polynomial as a product of simpler polynomials. In this article, we have provided a Q&A guide to help you understand the concept of factoring expressions and how to apply the perfect square trinomial formula. We have also provided some tips and tricks to help you avoid common mistakes when factoring expressions.