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 59E
To determine

To calculate: The simplified value of the expression (2x+y3)(2x+y+3) .

Expert Solution

Answer to Problem 59E

The value of the expression (2x+y3)(2x+y+3) is 4x2+4xy+y29 .

Explanation of Solution

Given information:

The expression (2x+y3)(2x+y+3) .

Formula used:

The special product formula of difference of squares to multiply the algebraic expressions is mathematically expressed as,

  (A+B)(AB)=A2B2

Special product of formula of perfect square of algebraic expressions which can be mathematically expressed as,

  (A+B)2=A2+2AB+B2

Calculation:

Consider the given expression (2x+y3)(2x+y+3) .

Recall the special product formula of difference of squares to multiply the algebraic expressions is mathematically expressed as,

  (A+B)(AB)=A2B2

Here, A=2x+y and B=3 .

Apply it,

  (2x+y3)(2x+y+3)=(2x+y)2(3)2=(2x+y)29

Now, recall the special product of formula of perfect square of algebraic expressions which can be mathematically expressed as,

  (A+B)2=A2+2AB+B2

Apply it to solve the expression (2x+y)2 ,

  (2x+y3)(2x+y+3)=(2x)2+2(2x)(y)+(y)29=4x2+4xy+y29

Thus, the value of the expression (2x+y3)(2x+y+3) is 4x2+4xy+y29 .

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