Simplify:

2 (5 + w) + 3 (w + 2)

16+5w

Step-by-step explanation:

2 (5 + w) + 3 (w + 2)

5+w evaluates to 5+w

Multiply 2 by 5+w

we multiply 2 by each term in 5+w term by term.

This is the distributive property of multiplication.

Multiply 2 and 5

1

2 * 5 = 10

Multiply 2 and w

Multiply 1 and w

The w just gets copied along.

w

2 * w = 2w

2 * (5+w) evaluates to 10+2w

w+2 evaluates to w+2

Multiply 3 by w+2

we multiply 3 by each term in w+2 term by term.

This is the distributive property of multiplication.

Multiply 3 and w

Multiply 1 and w

The w just gets copied along.

w

3 * w = 3w

Multiply 3 and 2

1

3 * 2 = 6

3 * (w+2) evaluates to 3w+6

To add the polynomials 10+2w and 3w+6 we try to add or combine terms in one polynomialwith any like terms in the other polynomial.

10 + 6 = 16

2w + 3w = 5w

The answer is 16+5w

2 * (5+w) + 3 * (w+2) evaluates to 16+5w

The final answer is

16+5w

5w+16