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Chapter 5: Problem 4

In each case, simplify the given expression, if possible. \(a b+b a\)

Short Answer

Expert verified
Question: Simplify the algebraic expression \(a b + b a\). Answer: \(2 a b\)

Step by step solution

01

Recognize Like Terms

In the given expression \(a b + b a\), the term \(a b\) and the term \(b a\) are both products of the variables 'a' and 'b'. We can see that these two terms involve the same variables, hence they are like terms.
02

Apply the Commutative Property of Addition

The Commutative Property of Addition states that for any two numbers (or terms) 'a' and 'b', we can change the order they are added in without affecting the sum: a + b = b + a. In our expression, \(a b + b a\), we can rewrite it as \(b a + a b\).
03

Apply the Commutative Property of Multiplication

The Commutative Property of Multiplication states that for any two numbers (or terms) 'a' and 'b', we can change the order they are multiplied in without affecting the product: a * b = b * a. In the rearranged expression, \(b a + a b\), the term \(b a\) can be rewritten as \(a b\), so the expression becomes \(a b + a b\).
04

Combine Like Terms

Since \(a b\) and \(a b\) are like terms, we can combine them by adding their coefficients. The coefficients of both terms are 1, so the coefficients are added together (1 + 1 = 2) and multiplied by the combined term. The simplified expression is \(2 a b\).

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Most popular questions from this chapter

Factorise \(\alpha^{2}-\beta^{2}\)

Factorise (a) \(16 x^{2}-4 x\), (b) \(11 y+121\), (c) \(a x^{2}-b x,\left(\right.\) d) \(c^{2}-2 c s\), (e) \(s^{2}-2 c s\).

Simplify (a) \(\frac{x}{4}+\frac{x}{5}\), (b) \(\frac{x}{4}+\frac{x}{5}+\frac{x}{6}\).

Simplify $$ \frac{a^{7} \times a^{-13}}{a^{-5}} $$

In each case, simplify the given expression, if possible. \( x^{2}+3 x+1\)
See all solutions

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