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

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

## To simplify: The expression 3(x+6)+4(2x−5).

Expert Solution

The expression 3(x+6)+4(2x5) is simplified as 11x2.

### Explanation of Solution

Consider the expression 3(x+6)+4(2x5).

Simplify the above expression as follows,

3(x+6)+4(2x5)=3x+3×6+4×2x4×5=3x+18+8x20=11x2

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

(b)

To determine

### To simplify: The expression (x+3)(4x−5).

Expert Solution

The expression (x+3)(4x5) is simplified as 4x2+7x15.

### Explanation of Solution

Consider the expression (x+3)(4x5).

Simplify the above expression as follows,

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

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

(c)

To determine

### To simplify: The expression (a−b)(a+b).

Expert Solution

The expression (ab)(a+b) is simplified as ab.

### Explanation of Solution

Consider the expression (ab)(a+b).

Simplify the above expression as follows,

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

Thus, the expression (ab)(a+b) is simplified as ab.

(d)

To determine

### To simplify: The expression (2x+3)2.

Expert Solution

The expression (2x+3)2 is simplified as 4x2+12x+9.

### Explanation of Solution

Consider the expression (2x+3)2.

Simplify the above expression as follows,

(2x+3)2=(2x)2+2×2x×3+32((a+b)2=a2+2ab+b2)=4x2+12x+9

Thus, the expression (2x+3)2 is simplified as 4x2+12x+9.

(e)

To determine

### To simplify: The expression (x+2)2.

Expert Solution

The expression (x+2)2 is simplified as x2+4x+4.

### Explanation of Solution

Consider the expression (x+2)2.

Simplify the above expression as follows,

(x+2)2=(x)2+2×x×2+22((a+b)2=a2+2ab+b2)=x2+4x+4

Thus, the expression (x+2)2 is simplified as x2+4x+4.

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