What expression is equivalent to 2.8k-8.4
The Correct answer and Explanation is:
The expression 2.8k−8.42.8k – 8.42.8k−8.4 can be simplified by factoring out the common coefficient, leading to the equivalent expression:2.8(k−3)\boxed{2.8(k – 3)}2.8(k−3)
Explanation
To understand how to derive the equivalent expression from 2.8k−8.42.8k – 8.42.8k−8.4, let’s break it down step by step.
- Identify Common Factors: The first step in simplifying algebraic expressions is to identify any common factors. In this case, both terms in the expression share a common coefficient, which is 2.82.82.8. This coefficient can be factored out from both terms.
- Factoring Out the Coefficient: We can rewrite the expression by factoring out 2.82.82.8:
- The first term 2.8k2.8k2.8k can be rewritten as 2.8×k2.8 \times k2.8×k.
- The second term −8.4-8.4−8.4 can be rewritten in terms of 2.82.82.8: since −8.4-8.4−8.4 is equal to 2.82.82.8 multiplied by −3-3−3 (because 2.8×−3=−8.42.8 \times -3 = -8.42.8×−3=−8.4), we can express −8.4-8.4−8.4 as 2.8×−32.8 \times -32.8×−3.
- Rewriting the Expression: By factoring 2.82.82.8 out of both terms, we get:2.8k−8.4=2.8(k)+2.8(−3)2.8k – 8.4 = 2.8(k) + 2.8(-3)2.8k−8.4=2.8(k)+2.8(−3)This simplifies to:2.8(k−3)2.8(k – 3)2.8(k−3)
- Understanding the Implications: Factoring an expression like 2.8(k−3)2.8(k – 3)2.8(k−3) can be beneficial in various mathematical contexts. For instance, it makes it easier to analyze the expression, find roots, or understand its behavior as a function. The factored form reveals that the expression is zero when k=3k = 3k=3, which can be particularly useful in solving equations or graphing.
- Conclusion: Therefore, while 2.8k−8.42.8k – 8.42.8k−8.4 and 2.8(k−3)2.8(k – 3)2.8(k−3) are equivalent expressions, the factored form is often more convenient for further mathematical operations, providing clarity and insight into the relationship between the variables involved.