Problem 95 Evaluate each expression without... [FREE SOLUTION]

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Chapter 1: Problem 95

Evaluate each expression without a calculator Use a calculator to check. $$3(-2)^{2}-5(-2)+4$$

Short Answer

Expert verified

Step by step solution

- Evaluate the exponent

Calculate $(-2)^2$. When squaring a negative number, the result is positive. So, $(-2)^2 = 4$.

- Multiply by the first coefficient

Multiply the result of the exponent by 3: $3 \times 4 = 12$.

- Multiply the second term

Multiply $-5$ by $-2$: $-5 \times -2 = 10$.

- Add the constant

Add 4 to the result.

- Sum the terms

Combine all the results: $12 + 10 + 4$. The sum is 26.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponents

Exponents are an essential concept in mathematics and involve raising a number to the power of another number. For instance, in the exercise, we have $(-2)^2$. Here, $2$ is the exponent, and it tells us how many times the base number (which is $-2$) is multiplied by itself. When squaring a negative number, you multiply it by itself: $(-2) \times (-2) = 4$. Remember, multiplying two negative numbers always gives a positive result. So, $(-2)^2 = 4$. Exponents help simplify expressions and make calculations easier.

Negative Numbers

Negative numbers are numbers less than zero. They can be tricky, especially when performing operations like multiplication. In our exercise, we deal with both negative and positive numbers. When you multiply two negative numbers, the result is always positive. For example, in step 3 of the solution, we multiply $-5$ by $-2$. Since both numbers are negative, multiplying them gives a positive result: $-5 \times -2 = 10$. Understanding how negative numbers interact during calculations is crucial for correctly evaluating expressions.

Multiplication

Multiplication is a basic arithmetic operation that combines two numbers to get a product. In the provided solution, there are two main multiplication steps. First, after calculating the exponent, multiply it by the coefficient: $3 \times 4 = 12$. Second, multiply $-5$ by $-2$: $-5 \times -2 = 10$. It's important to follow the correct order of operations (PEMDAS/BODMAS), which tells us to perform exponents first, then multiplication, ensuring our calculations are accurate.

Summation

Summation involves adding terms together. In the final step of our solution, we combine the results of previous steps: $12$ from the first multiplication, $10$ from the second multiplication, and $4$, a constant. Adding these together gives us the final result: $12 + 10 + 4 = 26$. Summation ensures that all components of the expression are accounted for and added correctly, resulting in the final value of the polynomial.

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91影视

Evaluate each expression without a calculator Use a calculator to check. $$3(-2)^{2}-5(-2)+4$$

Short Answer

Step by step solution

- Evaluate the exponent

- Multiply by the first coefficient

- Multiply the second term

- Add the constant

- Sum the terms

Key Concepts

Exponents

Negative Numbers

Multiplication

Summation

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