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 44E
To determine

To calculate: The simplified value of the expression (3+2y)3 .

Expert Solution

Answer to Problem 44E

The value of the expression (3+2y)3 is 8y3+36y2+54y+27 .

Explanation of Solution

Given information:

The expression (3+2y)3 .

Formula used:

The special product formula of perfect cube to multiply the algebraic expressions is mathematically expressed as,

  (A+B)3=A3+3AB(A+B)+B3

Calculation:

Consider the given expression (3+2y)3 .

Recall the special product formula of perfect cube to multiply the algebraic expressions is mathematically expressed as,

  (A+B)3=A3+3AB(A+B)+B3

Apply it,

  (3+2y)3=(3)3+3(3)(2y)(3+2y)+(2y)3=27+18y(3+2y)+8y3=27+54y+36y2+8y3=8y3+36y2+54y+27

Thus, the value of the expression (3+2y)3 is 8y3+36y2+54y+27 .

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