BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.3, Problem 48E
To determine

To calculate: The simplified value of the expression (1+2x)(x23x+1) .

Expert Solution

Answer to Problem 48E

The value of the expression (1+2x)(x23x+1) is 2x35x2x+1 .

Explanation of Solution

Given information:

The expression (1+2x)(x23x+1) .

Formula used:

To multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

  (a+b)(c+d)=a(c+d)+b(c+d)

Calculation:

Consider the given expression (1+2x)(x23x+1) .

Recall the to multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

  (a+b)(c+d)=a(c+d)+b(c+d)

Apply it,

  (1+2x)(x23x+1)=1(x23x+1)+2x(x23x+1)=1x2+1(3x)+11+2xx2+2x(3x)+2x1=x23x+1+2x36x2+2x

Combine the like terms and simplify it further as,

  (1+2x)(x23x+1)=x23x+1+2x36x2+2x=2x3+(6x2+x2)+(3x+2x)+1=2x35x2x+1

Thus, the value of the expression (1+2x)(x23x+1) is 2x35x2x+1 .

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