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Chapter 1: Problem 396

Evaluate each expression. \((y+z)^{2}\) when \(y=-3, z=15\)

Short Answer

Expert verified
144

Step by step solution

01

Substitute the Given Values

Replace the variables in the expression with the provided values. Given: \( y = -3 \) and \( z = 15 \). The expression \( (y+z)^{2} \) becomes \( (-3+15)^{2} \).
02

Simplify Inside the Parentheses

Simplify the expression inside the parentheses first: \( -3 + 15 = 12 \). The expression now is \( 12^{2} \).
03

Evaluate the Square

Calculate the square of 12: \( 12^{2} = 144 \).

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Key Concepts

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

substitution method
The substitution method is a fundamental concept in algebra. It involves replacing variables in an expression with their given values. For example, given the expression \((y+z)^{2}\) and the values \(y = -3\) and \(z = 15\):
The first step is to substitute \(y\) and \(z\) in the original expression. It transforms from \((y+z)^{2}\) to \((-3 + 15)^{2}\).
This method simplifies complex algebraic expressions by focusing on one variable at a time.
simplifying expressions
Simplifying expressions is crucial for solving algebraic problems efficiently.
After substitution, the next step in algebra is to simplify the expression inside the parentheses. This helps streamline the problem by reducing it to a simpler form.
In our example, after substituting \(y = -3\) and \(z = 15\), we have \((-3 + 15)^{2}\).
The next step is to simplify \(-3 + 15\), which is equal to 12. The expression now reads \(12^{2}\).
Simplifying expressions not only makes calculations easier but also reduces the risk of errors.
squaring numbers
Squaring numbers means multiplying a number by itself. This concept is essential in many areas of mathematics.
In our example, the simplified expression is \(12^{2}\).
To square 12, you multiply 12 by 12, which equals 144. Mathematically, it's represented as:
\[12^{2} = 12 \times 12 = 144\]
Squaring numbers often occurs in algebra, geometry, and real-world applications.
Practicing this process helps you become more confident in evaluating and simplifying squared expressions.

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