Simplify the expression.EXAMPLE 3Simplify each expression by combining like terms.a. 7x −...

Simplify the expression.

EXAMPLE 3

Simplify each expression by combining like terms.

a. 7x − 3x

b. 10y2 + y2

c. 8x2 + 2x − 3x

d. 8x2 + 2x − 3x

Solution

a. 7x − 3x = (7 − 3)x = 4x

b. 10y2 + y2 = 10y2 + 1y2 = (10 + 1)y2 = 11y2

c. 8x2 + 2x − 3x = 8x2 + (2 − 3)x = 8x2 − x

d. 9n2 − 5n2 + n2 = 19 − 5 + 12n2 = 5n2

EXAMPLE 4

Simplify each expression by combining like terms.

a. 2x + 3x + 5 + 2

b. −5a − 3 + a + 2

c. 4y − 3y2

d. 2.3x + 5x − 6

e.

Solution

a.

b.

c. 4y − 3y2 These two terms cannot be combined because they are unlike terms.

d.

e.

EXAMPLE 5

Find each product by using the distributive property to remove parentheses.

a. 5(3x + 2)

b. −21y + 0.3z − 12

c. − (9x + y − 2z + 6)

Solution

a.

b.

c.

EXAMPLE 6

Simplify each expression.

a. 3(2x − 5) + 1

b. −2(4x + 7) − (3x − 1)

c. 9 + 3(4x − 10)

Solution

a.

b.

c.

EXAMPLE 7

Write the phrase below as an algebraic expression. Then simplify if possible.

“Subtract 4x − 2 from 2x − 3.”

Solution

“Subtract 4x − 2 from 2x − 3” translates to 12x − 32 − 14x − 22. Next, simplify the algebraic expression.

3(2x − 5) −5(x − 4)