Simplify The Expression: 9 K 2 + 18 K − 40 9k^2 + 18k - 40 9 K 2 + 18 K − 40

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms and rearranging the expression to make it easier to work with. In this article, we will simplify the expression 9k2+18k−409k^2 + 18k - 40.

Understanding the Expression

The given expression is a quadratic expression in the form of ax2+bx+cax^2 + bx + c. Here, a=9a = 9, b=18b = 18, and c=−40c = -40. To simplify this expression, we need to combine like terms and factor out any common factors.

Step 1: Factor Out the Greatest Common Factor (GCF)

The first step in simplifying the expression is to factor out the greatest common factor (GCF) of the three terms. In this case, the GCF is 1, since there is no common factor that divides all three terms.

9k^2 + 18k - 40 = 1(9k^2 + 18k - 40)

Step 2: Combine Like Terms

The next step is to combine like terms. In this expression, the like terms are the terms that have the same variable and exponent. In this case, the like terms are 9k29k^2 and 18k18k.

9k^2 + 18k - 40 = 9k^2 + 18k - 40

However, we can rewrite 18k18k as 9k⋅2k9k \cdot 2k.

9k^2 + 18k - 40 = 9k^2 + 9k \cdot 2k - 40

Now, we can factor out the common factor of 9k9k from the first two terms.

9k^2 + 18k - 40 = 9k(k + 2k) - 40

Simplifying further, we get:

9k^2 + 18k - 40 = 9k(k + 2k) - 40
= 9k(3k) - 40
= 27k^2 - 40

Step 3: Factor the Expression

Now that we have simplified the expression, we can factor it further. In this case, we can factor the expression as a difference of squares.

27k^2 - 40 = (3k)^2 - 8^2
= (3k + 8)(3k - 8)

Therefore, the simplified expression is:

9k^2 + 18k - 40 = (3k + 8)(3k - 8)

Conclusion

In this article, we simplified the expression 9k2+18k−409k^2 + 18k - 40 by combining like terms and factoring out common factors. We first factored out the greatest common factor (GCF) of 1, then combined like terms, and finally factored the expression as a difference of squares. The simplified expression is (3k+8)(3k−8)(3k + 8)(3k - 8).

Final Answer

Introduction

In our previous article, we simplified the expression 9k2+18k−409k^2 + 18k - 40 by combining like terms and factoring out common factors. In this article, we will answer some frequently asked questions (FAQs) related to the simplification of this expression.

Q: What is the greatest common factor (GCF) of the three terms in the expression?

A: The greatest common factor (GCF) of the three terms in the expression is 1, since there is no common factor that divides all three terms.

Q: How do you combine like terms in the expression?

A: To combine like terms in the expression, we need to identify the terms that have the same variable and exponent. In this case, the like terms are 9k29k^2 and 18k18k. We can rewrite 18k18k as 9k⋅2k9k \cdot 2k and then factor out the common factor of 9k9k from the first two terms.

Q: What is the difference of squares formula?

A: The difference of squares formula is:

a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)

In our previous article, we used this formula to factor the expression 27k2−4027k^2 - 40 as a difference of squares.

Q: How do you factor a quadratic expression?

A: To factor a quadratic expression, we need to look for two binomials whose product is equal to the original expression. In this case, we factored the expression 9k2+18k−409k^2 + 18k - 40 as (3k+8)(3k−8)(3k + 8)(3k - 8).

Q: What is the final answer to the expression?

A: The final answer to the expression is (3k+8)(3k−8)(3k + 8)(3k - 8).

Q: Can you provide more examples of simplifying quadratic expressions?

A: Yes, here are a few more examples of simplifying quadratic expressions:

  • x2+5x+6=(x+3)(x+2)x^2 + 5x + 6 = (x + 3)(x + 2)
  • y2−4y−5=(y−5)(y+1)y^2 - 4y - 5 = (y - 5)(y + 1)
  • z2+2z−15=(z+5)(z−3)z^2 + 2z - 15 = (z + 5)(z - 3)

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to the simplification of the expression 9k2+18k−409k^2 + 18k - 40. We covered topics such as the greatest common factor (GCF), combining like terms, the difference of squares formula, factoring quadratic expressions, and providing more examples of simplifying quadratic expressions.

Final Answer

The final answer is: (3k+8)(3k−8)\boxed{(3k + 8)(3k - 8)}

Additional Resources

For more information on simplifying quadratic expressions, please refer to the following resources:

  • Khan Academy: Simplifying Quadratic Expressions
  • Mathway: Simplifying Quadratic Expressions
  • Wolfram Alpha: Simplifying Quadratic Expressions

We hope this article has been helpful in understanding how to simplify quadratic expressions. If you have any further questions or need additional help, please don't hesitate to ask.