# The addition of algebraic expression 3 ( x + 6 ) + 4 ( 2 x − 5 ) .

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1, Problem 6T

(a)

To determine

## The addition of algebraic expression 3(x+6)+4(2x−5) .

Expert Solution

The addition of expression 3(x+6)+4(2x5) is 11x2 .

### Explanation of Solution

Given:

The algebraic expression is 3(x+6)+4(2x5) .

Calculation:

Addition of given algebraic expression is,

3(x+6)+4(2x5)=3x+18+8x20=11x2

Thus, the addition of expression 3(x+6)+4(2x5) is 11x2 .

(b)

To determine

### The multiplication of algebraic expression (x+3)(4x−5) .

Expert Solution

The multiplication of expression (x+3)(4x5) is 4x2+7x15 .

### Explanation of Solution

Given:

The algebraic expression is (x+3)(4x5) .

Calculation:

Multiplication of given algebraic expression is,

(x+3)(4x5)=x(4x5)+3(4x5)=(x4xx5)+(34x35)=(4x25x)+(12x15)=4x2+7x15

Thus, the multiplication of expression (x+3)(4x5) is 4x2+7x15 .

(c)

To determine

### The multiplication of algebraic expression (a+b)(a−b) .

Expert Solution

The multiplication of expression (a+b)(ab) is ab .

### Explanation of Solution

Given:

The algebraic expression is (a+b)(ab) .

Calculation:

Special product formula for algebraic expression is,

(A+B)(AB)=A2B2

The algebraic expression shows that sum and difference of same terms so use special product formula.

Substitute a for A and b for B in the above formula,

(a+b)(ab)=(a)2(b)2=ab

Thus, the multiplication of expression (a+b)(ab) is ab .

(d)

To determine

### The square of a sum of algebraic expression (2x+3)2 .

Expert Solution

The square of a sum of expression (2x+3)2 is 4x2+12x+9 .

### Explanation of Solution

Given:

The algebraic expression is (2x+3)2 .

Calculation:

Special product formula of square of sum for algebraic expression is,

(A+B)2=A2+2AB+B2

Substitute 2x for A and 3 for B in the above formula,

(2x+3)2=(2x)2+22x3+(3)2=4x2+12x+9

Thus, the square of a sum of expression (2x+3)2 is 4x2+12x+9 .

(e)

To determine

### The cube of a sum of algebraic expression (x+2)3 .

Expert Solution

The square of a sum of expression (x+2)3 is x3+6x2+12x+8 .

### Explanation of Solution

Given:

The algebraic expression is (x+2)3 .

Calculation:

Special product formula of cube of sum for algebraic expression is,

(A+B)3=A3+3A2B+3AB2+B3

Substitute x for A and 2 for B in the above formula,

(x+2)3=(x)3+3x22+3x22+(2)3=x3+6x2+12x+8

Thus, the square of a sum of expression (x+2)3 is x3+6x2+12x+8 .

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