/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 114 An expression is \((x-4)(x-3)\).... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 114

An expression is \((x-4)(x-3)\). Evaluate this expression when \(x=4\).

Short Answer

Expert verified
0

Step by step solution

01

Identify the given expression

The expression given is \((x-4)(x-3)\). You will substitute the value of x to evaluate the expression.
02

Substitute the value of x

Given that \(x=4\), substitute 4 into the expression: \((4-4)(4-3)\).
03

Simplify each term inside the parentheses

Evaluate the terms inside the parentheses: \(4-4 = 0\) and \(4-3 = 1\).
04

Multiply the simplified terms

Now multiply the results: \(0 \times 1 = 0\).
05

Conclusion

The value of the expression \((x-4)(x-3)\) when \(x=4\) is \(0\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Substitution in Algebra
Substitution in algebra is a fundamental process that involves replacing a variable with a given value. This makes it easier to simplify or solve expressions.
For example, in the given expression \((x-4)(x-3)\), we are asked to evaluate it when \(x=4\). To do this, we substitute 4 wherever we see \(x\) in the expression.
Substitution simply means:
  • Identify the variable in the expression.
  • Replace the variable with the given value.
  • Proceed to simplify the new, numerical expression.
This process helps to turn a more complex expression into a simpler one, like turning variables into numbers, which are easier to handle.
Simplifying Expressions
Simplifying expressions is a crucial step to making algebraic problems more manageable. Simplification usually involves performing basic arithmetic operations:
  • Addition and subtraction
  • Multiplication and division
Once you substitute values into the expression, your next step is to simplify the terms inside any parentheses. For example, after substituting \(x=4\) into \((x-4)(x-3)\), we simplify each term inside the parentheses:
  • \(4-4=0\)
  • \(4-3=1\)
By simplifying these, the expression becomes much simpler, allowing for further operations like multiplication.
Algebraic Multiplication
Multiplication in algebra involves combining simplified terms to find the overall value of an expression. In this particular problem, after substituting \(x=4\) and simplifying the terms inside the parentheses, you get:\((0)(1)\).
The final step involves multiplying these terms together. In this case, multiplication is straightforward:
\(0 \times 1 = 0\).

Here鈥檚 a quick reminder when multiplying algebraic terms:
  • Always simplify inside parentheses first.
  • Then multiply the simplified terms.
  • Remember, any number multiplied by zero is zero.
Therefore, the value of the expression \((x-4)(x-3)\) when \(x=4\) is 0.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The width of a rectangle is \(7 \mathrm{ft}\) less than its length. Its area is \(120 \mathrm{ft}^{2}\).

(a) solve. (b) check. $$ 6 v^{2}+31 v+35=0 $$

Solve: \(9 x=0\)

Explain why the solutions of the equation \(2(x+5)(x-1)=0\) are the same as the solutions of the equation \((2 x+10)(x-1)=0\).

(a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Factor \(5 x^{2}+500 y^{2}\) completely. Incorrect Answer: \(5 x^{2}+500 y^{2}\) $$ \begin{aligned} &=5\left(x^{2}+100 y^{2}\right) \\ &=5(x+10 y)(x+10 y) \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.